Feature-based Time Series Forecasting

# Feature-based Time Series Forecasting
### Thiyanga S. Talagala
### Forecasting for Social Good (F4SG): Democratising Forecasting

---

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  top: 50%;
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### Content

- Time series features

- feasts: *F*eature *E*xtraction *A*nd *S*tatistics for *T*ime *S*eries

- Feature-based time series forecasting

- Other applications

- Data visualization

- Anomaly detection
    
- What did we learn?

- Where to go from here?

---
background-image: url(img/vaccine.png)
background-size: cover

---

---

class: inverse, center, middle
background-image: url(img/jhu.png)
background-position: 50% 60%1

background-size: contain

Let's visualize the coronavirus pandemic!

---

background-image: url(img/coronavirus.png)
background-size: 90px
background-position: 100% 6%

# Data: coronavirus package

```r
install.packages("coronavirus")
# devtools::install_github("RamiKrispin/coronavirus")
```

```r
library(coronavirus)
head(coronavirus, 8)
```

```
        date province             country       lat      long      type cases
1 2020-01-22                  Afghanistan  33.93911  67.70995 confirmed     0
2 2020-01-22                      Albania  41.15330  20.16830 confirmed     0
3 2020-01-22                      Algeria  28.03390   1.65960 confirmed     0
4 2020-01-22                      Andorra  42.50630   1.52180 confirmed     0
5 2020-01-22                       Angola -11.20270  17.87390 confirmed     0
6 2020-01-22          Antigua and Barbuda  17.06080 -61.79640 confirmed     0
7 2020-01-22                    Argentina -38.41610 -63.61670 confirmed     0
8 2020-01-22                      Armenia  40.06910  45.03820 confirmed     0
```

---

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104 country: Afghanistan","date: 2020-10-27 cases: 95 country: Afghanistan","date: 2020-10-28 cases: 113 country: Afghanistan","date: 2020-10-29 cases: 123 country: Afghanistan","date: 2020-10-30 cases: 66 country: Afghanistan","date: 2020-10-31 cases: 91 country: Afghanistan","date: 2020-11-01 cases: 76 country: Afghanistan","date: 2020-11-02 cases: 132 country: Afghanistan","date: 2020-11-03 cases: 95 country: Afghanistan","date: 2020-11-04 cases: 86 country: Afghanistan","date: 2020-11-05 cases: 121 country: Afghanistan","date: 2020-11-06 cases: 40 country: Afghanistan","date: 2020-11-07 cases: 58 country: Afghanistan","date: 2020-11-08 cases: 126 country: Afghanistan","date: 2020-11-09 cases: 138 country: Afghanistan","date: 2020-11-10 cases: 166 country: Afghanistan","date: 2020-11-11 cases: 146 country: Afghanistan","date: 2020-11-12 cases: 186 country: Afghanistan","date: 2020-11-13 cases: 174 country: Afghanistan","date: 2020-11-14 cases: 66 country: Afghanistan","date: 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2020-09-04 cases: 75 country: Cabo Verde","date: 2020-09-05 cases: 75 country: Cabo Verde","date: 2020-09-06 cases: 55 country: Cabo Verde","date: 2020-09-07 cases: 28 country: Cabo Verde","date: 2020-09-08 cases: 42 country: Cabo Verde","date: 2020-09-09 cases: 73 country: Cabo Verde","date: 2020-09-10 cases: 84 country: Cabo Verde","date: 2020-09-11 cases: 94 country: Cabo Verde","date: 2020-09-12 cases: 60 country: Cabo Verde","date: 2020-09-13 cases: 102 country: Cabo Verde","date: 2020-09-14 cases: 26 country: Cabo Verde","date: 2020-09-15 cases: 65 country: Cabo Verde","date: 2020-09-16 cases: 74 country: Cabo Verde","date: 2020-09-17 cases: 85 country: Cabo Verde","date: 2020-09-18 cases: 78 country: Cabo Verde","date: 2020-09-19 cases: 45 country: Cabo Verde","date: 2020-09-20 cases: 71 country: Cabo Verde","date: 2020-09-21 cases: 24 country: Cabo Verde","date: 2020-09-22 cases: 56 country: Cabo Verde","date: 2020-09-23 cases: 75 country: Cabo Verde","date: 2020-09-24 cases: 67 country: Cabo Verde","date: 2020-09-25 cases: 149 country: Cabo Verde","date: 2020-09-26 cases: 73 country: Cabo Verde","date: 2020-09-27 cases: 70 country: Cabo Verde","date: 2020-09-28 cases: 46 country: Cabo Verde","date: 2020-09-29 cases: 83 country: Cabo Verde","date: 2020-09-30 cases: 124 country: Cabo Verde","date: 2020-10-01 cases: 102 country: Cabo Verde","date: 2020-10-02 cases: 79 country: Cabo Verde","date: 2020-10-03 cases: 91 country: Cabo Verde","date: 2020-10-04 cases: 64 country: Cabo Verde","date: 2020-10-05 cases: 73 country: Cabo Verde","date: 2020-10-06 cases: 85 country: Cabo Verde","date: 2020-10-07 cases: 106 country: Cabo Verde","date: 2020-10-08 cases: 93 country: Cabo Verde","date: 2020-10-09 cases: 92 country: Cabo Verde","date: 2020-10-10 cases: 104 country: Cabo Verde","date: 2020-10-11 cases: 159 country: Cabo Verde","date: 2020-10-12 cases: 83 country: Cabo Verde","date: 2020-10-13 cases: 99 country: Cabo Verde","date: 2020-10-14 cases: 117 country: 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2020-11-24 cases: 98 country: Cabo Verde","date: 2020-11-25 cases: 126 country: Cabo Verde","date: 2020-11-26 cases: 44 country: Cabo Verde","date: 2020-11-27 cases: 56 country: Cabo Verde","date: 2020-11-28 cases: 74 country: Cabo Verde","date: 2020-11-29 cases: 47 country: Cabo Verde","date: 2020-11-30 cases: 14 country: Cabo Verde","date: 2020-12-01 cases: 55 country: Cabo Verde","date: 2020-12-02 cases: 51 country: Cabo Verde","date: 2020-12-03 cases: 71 country: Cabo Verde","date: 2020-12-04 cases: 58 country: Cabo Verde","date: 2020-12-05 cases: 40 country: Cabo Verde","date: 2020-12-06 cases: 27 country: Cabo Verde","date: 2020-12-07 cases: 35 country: Cabo Verde","date: 2020-12-08 cases: 20 country: Cabo Verde","date: 2020-12-09 cases: 74 country: Cabo Verde","date: 2020-12-10 cases: 11 country: Cabo Verde","date: 2020-12-11 cases: 59 country: Cabo Verde","date: 2020-12-12 cases: 40 country: Cabo Verde","date: 2020-12-13 cases: 55 country: Cabo Verde","date: 2020-12-14 cases: 4 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53 country: Cabo Verde","date: 2021-02-14 cases: 41 country: Cabo Verde","date: 2021-02-15 cases: 20 country: Cabo Verde","date: 2021-02-16 cases: 24 country: Cabo Verde","date: 2021-02-17 cases: 63 country: Cabo Verde","date: 2021-02-18 cases: 37 country: Cabo Verde","date: 2021-02-19 cases: 63 country: Cabo Verde","date: 2021-02-20 cases: 51 country: Cabo Verde","date: 2021-02-21 cases: 49 country: Cabo Verde","date: 2021-02-22 cases: 24 country: Cabo Verde","date: 2021-02-23 cases: 17 country: Cabo Verde","date: 2021-02-24 cases: 72 country: Cabo Verde","date: 2021-02-25 cases: 40 country: Cabo Verde","date: 2021-02-26 cases: 52 country: Cabo Verde","date: 2021-02-27 cases: 71 country: Cabo Verde","date: 2021-02-28 cases: 76 country: Cabo Verde","date: 2021-03-01 cases: 32 country: Cabo Verde","date: 2021-03-02 cases: 51 country: Cabo Verde","date: 2021-03-03 cases: 75 country: Cabo Verde","date: 2021-03-04 cases: 63 country: Cabo Verde","date: 2021-03-05 cases: 62 country: Cabo 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Korea, South","date: 2020-10-02 cases: 75 country: Korea, South","date: 2020-10-03 cases: 64 country: Korea, South","date: 2020-10-04 cases: 73 country: Korea, South","date: 2020-10-05 cases: 75 country: Korea, South","date: 2020-10-06 cases: 114 country: Korea, South","date: 2020-10-07 cases: 69 country: Korea, South","date: 2020-10-08 cases: 54 country: Korea, South","date: 2020-10-09 cases: 72 country: Korea, South","date: 2020-10-10 cases: 58 country: Korea, South","date: 2020-10-11 cases: 97 country: Korea, South","date: 2020-10-12 cases: 102 country: Korea, South","date: 2020-10-13 cases: 84 country: Korea, South","date: 2020-10-14 cases: 99 country: Korea, South","date: 2020-10-15 cases: 47 country: Korea, South","date: 2020-10-16 cases: 73 country: Korea, South","date: 2020-10-17 cases: 91 country: Korea, South","date: 2020-10-18 cases: 76 country: Korea, South","date: 2020-10-19 cases: 58 country: Korea, South","date: 2020-10-20 cases: 91 country: Korea, South","date: 2020-10-21 cases: 119 country: Korea, South","date: 2020-10-22 cases: 155 country: Korea, South","date: 2020-10-23 cases: 77 country: Korea, South","date: 2020-10-24 cases: 61 country: Korea, South","date: 2020-10-25 cases: 119 country: Korea, South","date: 2020-10-26 cases: 88 country: Korea, South","date: 2020-10-27 cases: 103 country: Korea, South","date: 2020-10-28 cases: 125 country: Korea, South","date: 2020-10-29 cases: 114 country: Korea, South","date: 2020-10-30 cases: 126 country: Korea, South","date: 2020-10-31 cases: 124 country: Korea, South","date: 2020-11-01 cases: 97 country: Korea, South","date: 2020-11-02 cases: 75 country: Korea, South","date: 2020-11-03 cases: 118 country: Korea, South","date: 2020-11-04 cases: 125 country: Korea, South","date: 2020-11-05 cases: 145 country: Korea, South","date: 2020-11-06 cases: 89 country: Korea, South","date: 2020-11-07 cases: 143 country: Korea, South","date: 2020-11-08 cases: 126 country: Korea, South","date: 2020-11-09 cases: 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2020-11-01 cases: 0 country: Kyrgyzstan","date: 2020-11-02 cases: 1001 country: Kyrgyzstan","date: 2020-11-03 cases: 895 country: Kyrgyzstan","date: 2020-11-04 cases: 535 country: Kyrgyzstan","date: 2020-11-05 cases: 0 country: Kyrgyzstan","date: 2020-11-06 cases: 439 country: Kyrgyzstan","date: 2020-11-07 cases: 556 country: Kyrgyzstan","date: 2020-11-08 cases: 515 country: Kyrgyzstan","date: 2020-11-09 cases: 571 country: Kyrgyzstan","date: 2020-11-10 cases: 970 country: Kyrgyzstan","date: 2020-11-11 cases: 0 country: Kyrgyzstan","date: 2020-11-12 cases: 527 country: Kyrgyzstan","date: 2020-11-13 cases: 567 country: Kyrgyzstan","date: 2020-11-14 cases: 499 country: Kyrgyzstan","date: 2020-11-15 cases: 1030 country: Kyrgyzstan","date: 2020-11-16 cases: 0 country: Kyrgyzstan","date: 2020-11-17 cases: 486 country: Kyrgyzstan","date: 2020-11-18 cases: 425 country: Kyrgyzstan","date: 2020-11-19 cases: 422 country: Kyrgyzstan","date: 2020-11-20 cases: 386 country: Kyrgyzstan","date: 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---
class: center, middle

# What problems do you see in the plot?

---

background-image: url(img/tukey.jpeg)
background-size: 200px
background-position: 100% 6%

# Time series features

- **Cognostics**: **Co**mputer-aided dia**gnostics** (John W. Tukey, 1985)

- Characteristics of time series

- Summary measures of time series

**Basic Principle**

- Transform a given time series `$y=\{y_1, y_2, \cdots, y_n\}$` into a feature vector `$F = (f_1(y), f_2(y), \cdots, f_p(y))'$`.

---

## Examples of time series features

- length

- strength of trend

- strength of seasonality

- lag-1 autocorrelation

- spectral entropy

- proportion of zeros

- spikiness

]

- curvature

- linearity

- stability

- number of peaks

- parameter estimates of Holt-Winters' additive method

- unit root test statistics

]

---
.pull-left[
#### Time-domain representation

![](index_files/figure-html/unnamed-chunk-4-1.png)

]

#### Feature-domain representation

![](index_files/figure-html/unnamed-chunk-5-1.png)

]

---

### Time-domain representation

```
$N0001
Time Series:
Start = 1975 
End = 1988 
Frequency = 1 
 [1]  940.66 1084.86 1244.98 1445.02 1683.17 2038.15 2342.52 2602.45 2927.87
[10] 3103.96 3360.27 3807.63 4387.88 4936.99

$N0633
Time Series:
Start = 1974 
End = 1989 
Frequency = 1 
 [1] 6664 7719 6750 6638 6666 6497 5867 6895 6077 6796 7488 7285 8014 8731 7650
[16] 7200

$N0625
Time Series:
Start = 1973 
End = 1989 
Frequency = 1 
 [1] 1570 2270 2246 2072 2024 2120 2522 2560 2592 2576 2916 2874 3398 3580 3770
[16] 4222 4486

$N0645
Time Series:
Start = 1955 
End = 1986 
Frequency = 1 
 [1] 6030 5070 5970 7870 5490 7600 5620 5040 6140 5410 8880 8130 6850 6990 6180
[16] 6310 5080 7400 5790 6682 6582 4167 7165 7426 7290 6900 7459 7003 6226 7453
[31] 5009 6115

$N1912
      Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
1981 3959 3704 5149 5419 5151 6368 6427 5724 4809 4596 4454 4488
1982 3696 4103 5299 5156 5699 6326 5732 6029 5193 4888 4482 4417
1983 4539 3470 5358 5099 5979 6631 6163 6653 5648 4732 4429 3916
1984 4117 4636 4639 5033 5431 6100 6499 6716 4880 5206 4421 3897
1985 4479 4102 4301 5606 5762 5998 6279 5893 4825 4870 4088 3882
1986 4303 4065 4861 6173 5884 5856 5899 5293 4687 4796 3988 4080
1987 4048 4174 5353 5913 6196 6471 5950 5962 5203 4896 4085 4183
1988 3978 4371 5325 5928 5800 6568 6115 6202 5340 4983 4410 4531
1989 4630 4416 5290 5998 6153 6359 5826 6184 4989 5126 4668 4174
1990 4215 4284 5342 5109 6026 5835 5835 5876 4757 4920 4176 3886
1991 3987 3750 4591 5303 5822 5663

$N2012
        Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct
1979 2317.0 2265.0 2842.0 2485.0 2904.0 2781.5 2587.0 2734.5 2389.5 2657.0
1980 2273.0 2400.5 2582.5 2733.5 2951.0 3036.0 2871.0 2939.5 3004.0 3050.5
1981 2414.0 2564.5 3128.5 3303.5 3274.0 3609.0 3262.0 3309.0 3263.0 2998.5
1982 2413.5 2525.0 3055.5 3138.5 3294.5 3650.0 3131.0 3328.5 3242.5 2702.0
1983 2456.5 2594.0 3283.0 3384.0 3642.5 4043.0 3460.5 3771.5 3568.0 3284.5
1984 3122.5 3362.0 3803.5 3771.5 4196.0 4199.5 3925.5 4165.0 3722.0 3826.5
1985 3152.5 3106.0 3771.5 4326.5 4650.5 4402.5 4311.0 4321.5 4029.5 4102.0
1986 3493.0 3405.5 3800.0 4519.5 4569.0 4455.0 4313.5 4281.5 4207.5 4317.0
1987 3515.5 3808.0 4290.5 4566.0 4632.5 4719.0 4592.0 4508.0 4448.5 4524.0
1988 3621.5 3966.0 4633.5 4698.0 5012.5 5179.0 4556.5 4854.0 4663.0 4540.5
1989 3986.0 4086.0 4626.5 4789.0 5208.5 5301.0                            
        Nov    Dec
1979 2177.0 1870.0
1980 2381.5 2264.5
1981 2448.5 2202.0
1982 2378.0 2081.0
1983 2900.5 2529.5
1984 3165.0 2832.5
1985 3368.0 2855.0
1986 3300.5 3071.5
1987 3790.0 3438.0
1988 4098.5 3757.5
1989              
```

]

![](index_files/figure-html/unnamed-chunk-7-1.png)

]

---
### Feature-domain representation

```
# A tibble: 6 × 3
 trend seasonality id 
 <dbl> <dbl> <chr>
1 0.995 0 N0001
2 0.591 0 N0633
3 0.961 0 N0625
4 0.178 0 N0645
5 0.251 0.906 N1912
6 0.968 0.927 N2012
```
]

![](index_files/figure-html/unnamed-chunk-9-1.png)

]

---

## Features for all countries

```
# A tibble: 193 × 25
 country trend_strength seasonal_strengt… seasonal_peak_we… seasonal_trough…
 <chr> <dbl> <dbl> <dbl> <dbl>
 1 Afghanis… 0.870 0.260 6 5
 2 Albania 0.985 0.493 2 6
 3 Algeria 0.991 0.308 2 4
 4 Andorra 0.684 0.656 6 5
 5 Angola 0.914 0.380 1 6
 6 Antigua … 0.437 0.169 2 5
 7 Argentina 0.980 0.774 2 5
 8 Armenia 0.982 0.876 2 6
 9 Australia 0.833 0.271 1 3
10 Austria 0.984 0.712 2 6
# … with 183 more rows, and 20 more variables: spikiness <dbl>,
# linearity <dbl>, curvature <dbl>, stl_e_acf1 <dbl>, stl_e_acf10 <dbl>,
# acf1 <dbl>, acf10 <dbl>, diff1_acf1 <dbl>, diff1_acf10 <dbl>,
# diff2_acf1 <dbl>, diff2_acf10 <dbl>, season_acf1 <dbl>, pacf5 <dbl>,
# diff1_pacf5 <dbl>, diff2_pacf5 <dbl>, season_pacf <dbl>,
# zero_run_mean <dbl>, nonzero_squared_cv <dbl>, zero_start_prop <dbl>,
# zero_end_prop <dbl>
```

---

# Time-domain

![](index_files/figure-html/unnamed-chunk-11-1.png)

]

# Feature-space

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]

---

## Strength of trend

![](index_files/figure-html/unnamed-chunk-13-1.png)

]

`$$y_t = T_t + S_t + R_t$$`

`$$F_T = max \left(0, 1 - \frac{Var(R_t)}{Var(T_t + R_t)} \right)$$`

]

---

## Strength of seasonality

![](index_files/figure-html/unnamed-chunk-14-1.png)

]

`$$y_t = T_t + S_t + R_t$$`

`$$F_S = max \left(0, 1 - \frac{Var(R_t)}{Var(S_t + R_t)} \right)$$`

]

---

## *F*eature *E*xtraction *A*nd *S*tatistics for *T*ime *S*eries: *feasts*

You could install the stable version from CRAN:

```r
install.packages("feasts")
```

You can install the development version from GitHub with:

```r
# install.packages("remotes")
remotes::install_github("tidyverts/feasts")
```
]

![](img/feastlogo.png)
]

---

# Large-scale time series forecasting

---

---

---

# Feature-based time series forecasting

---

class: inverse, center, middle
background-image: url(img/f1.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f2.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f3.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f4.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f5.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f6.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f7.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f8.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f9.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f10.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f11.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f12.png)
background-size: contain

---
class: inverse, center, middle
background-image: url(img/f13.png)
background-size: contain

---

## Machine learning algorithms

- Random forest

- XGBoost

---
background-image: url(img/forest.jpg)
background-size: cover

# Random forest

---
background-image: url(img/rf1.png)
background-size: contain

## Random forest

---
background-image: url(img/rf2.png)
background-size: contain

## Random forest

---
background-image: url(img/rf3.png)
background-size: contain

## Random forest

---
background-image: url(img/rf4.png)
background-size: contain

## Random forest

---
background-image: url(img/rf5.png)
background-size: contain

---
background-image: url(img/rf6.png)
background-size: contain

---
background-image: url(img/rf7.png)
background-size: contain

---
background-image: url(img/rf8.png)
background-size: contain

---
background-image: url(img/rf9.png)
background-size: contain

---
background-image: url(img/rf10.png)
background-size: contain

---
background-image: url(img/rf11.png)
background-size: contain

---
background-image: url(img/rf12.png)
background-size: contain

---
background-image: url(img/rf13.png)
background-size: contain

---

### FFORMS: **F**eature-based **FOR**ecast **M**odel **S**election

]

```r
install.packages("seer")
#library(devtools)
#install_github("thiyangt/seer")
library(seer)
```

]

---
## seer package

**Training set**

```r
library(Mcomp)
data(M1)
yearly_m1 <- subset(M1, "yearly")
yearly_m1
```

```
M-Competition data: 181 YEARLY time series

Type of data
Period   DEMOGR INDUST MACRO1 MACRO2 MICRO1 MICRO2 MICRO3
  YEARLY     30     35     30     29     16     29     12
```

**Test set**

```r
data(M3)
yearly_m3 <- subset(M3, "yearly")
m3y <- M3[1:2]
m3y
```

```
        Type of data
Period   MICRO
  YEARLY     2
```

---
## seer package: `cal_features`

```
# A tibble: 181 × 25
 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
 1 0.442 0.0400 0.977 0.985 0.985 1.32e-6 4.46 0.705 -0.0603
 2 0.363 0.0790 0.894 0.988 0.989 1.54e-6 4.47 0.613 0.272 
 3 0.379 0.0160 0.858 0.987 0.989 1.13e-6 4.60 0.695 0.172 
 4 0.363 0.00201 1.32 0.982 0.957 8.96e-6 4.48 0.0735 -0.396 
 5 0.156 0.00112 0.446 0.993 0.973 1.80e-6 5.77 1.21 0.0113
 6 0.441 0.00774 0.578 0.986 0.975 3.31e-6 4.75 0.748 -0.385 
 7 0.118 0 0 0.943 0.975 4.95e-6 2.94 0.391 0.0868
 8 0.357 0 0 0.949 0.978 2.39e-6 3.11 -0.360 0.220 
 9 0.698 0 0 0.931 0.983 5.09e-6 2.74 0.381 0.198 
10 0.435 0.0188 1.05 0.987 0.956 8.44e-6 4.70 -1.57 0.445 
# … with 171 more rows, and 16 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>,
# diff2y_acf1 <dbl>, y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>,
# nonlinearity <dbl>, lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>,
# y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>, beta <dbl>
```

---
## seer package: `fcast_accuracy`

```r
accuracy_m1 <- fcast_accuracy(tslist=yearly_m1, 
 models= c("arima","ets","rw","rwd", "theta", "nn"), 
 database ="M1", cal_MASE, h=6, length_out = 1, fcast_save = TRUE)
accuracy_m1
```

```
$accuracy
            arima         ets         rw        rwd      theta         nn
YAF2  10.52761210 10.31902909 13.5242826 10.5276121 12.0883746 11.7435830
YAF3   5.71386709  7.70440875  7.7894900  5.2259645  6.2254631  6.7007725
YAF4   8.63359043  8.09141559 11.5563254  8.4401052  9.9527425 10.7851084
YAF5   2.94027818  3.55921826  3.8159137  2.0593759  3.3634957  5.6133026
YAF6  10.12704721 10.20979344 13.1853523 11.8011284 11.9567016 12.0371540
YAF7   5.54339312  3.59967847  7.7707855  5.6992117  6.7834130  7.9262836
YAF8   7.60049192 11.10059289 11.1004919  7.6004919  9.3402119 10.6301203
YAF9   6.84308990 10.34324932 10.3430899  6.8430899  8.7991545  3.6132285
YAF10  5.86529331  9.25760811  9.2574869  5.8652933  7.5936209  8.6301201
YAF11  1.23793267  1.63301650  0.8753143  1.2379327  0.8214250  1.3109470
YAF12  3.40072568  4.52700282  2.5459640  2.1821816  1.9823345  1.9063434
YAF13  3.92372789  4.57608592 13.8754910 10.4707713 12.3532647  4.8339202
YAF14  8.49703094  9.47041582 10.3081214  8.6474142  9.5188299 10.2193305
YAF15  4.36913758  1.96868734  2.2912143  4.3691376  3.4009541  2.2627787
YAF16  7.34633345  9.08427659  9.0842269  6.2573504  7.4701031  8.8633554
YAF17  1.20990669  1.11067633  2.4250935  1.2099067  0.6561892  0.5988013
YAM1   2.54683126  2.53579067  2.5468313  1.6143928  2.1537059  3.4117566
YAM2   4.25524677  4.90899829  5.0623649  3.0576324  4.0734154  7.6918735
YAM3   6.05683571  5.89014664  8.1461278  6.0568357  7.0407755  8.0639551
YAM4   1.19998236  1.20003498  1.1999824  2.2359992  1.7840516  1.4771940
YAM5   3.31794454  2.83506356  2.8350440  1.0886081  1.7970424  2.8181306
YAM6   1.47552380  1.16753611  2.0997057  1.4755238  0.4562984  0.3874757
YAM7   2.83313760  2.67867100  5.8312493  8.1481252  7.0284151  7.1772071
YAM8   1.80107203  1.80141438  0.8839303  1.5957746  0.8706297  1.5903707
YAM10  2.19130032  0.69600689  0.2018244  0.4169883  0.3389725  0.7754451
YAM11  1.27865397  1.08969165  1.0896916  1.1543688  1.1566558  1.3954503
YAM12  1.59902131  1.21865607  1.2372645  1.2561412  1.1928689  1.3476414
YAM13  1.21864476  1.27404616  1.3859609  1.4067800  1.2664949  1.2269422
YAM14  1.57735714  1.57730115  1.5773571  0.5354010  1.1179100  1.7157432
YAM15  1.36239732  1.34961897  1.3623973  0.9192394  1.0313569  1.0127594
YAM16  2.74727838  2.95328269  2.7472784  2.4252260  3.2005197  2.8531625
YAM17  1.93192037  1.33645073  1.9319204  1.4846981  1.0876595  2.8029327
YAM18  1.81862167  1.81446336  3.4247628  1.8186217  2.4413399  1.9152402
YAM19  6.40541465  6.23091817  5.7614896  4.8690052  6.5556919  6.2150511
YAM20  0.87905348  0.87905260  0.8790535  0.8586165  0.8152457  2.9254150
YAM21  7.15484924  6.82442652  4.8888714  4.3456730  6.4407452 10.4744798
YAM22  1.99880648  1.23012771  1.2301178  0.8267946  1.2035729  1.4810607
YAM23  2.16308213  1.34679107  3.0789946  0.6116472  1.5769453  1.4334564
YAM24  2.96436564  2.83000074  4.5744272  2.9643656  3.7487062  4.1406297
YAM25  2.69644785  2.67339693  3.0070651  2.6964478  2.4954923  3.3531287
YAM26  5.10341668  6.12705992  6.1270879  5.1034167  5.5170900  6.7712570
YAM27  5.99145614  6.42086150 12.1183489  9.0463863 10.6348135  9.0360042
YAM28  2.27016299  2.32372771  8.2290301  4.8541543  6.6341227  3.4607979
YAM29  0.67800479  1.60335901  1.6034519  1.9104025  1.6172736  3.4614011
YAM30  2.58534179  3.71125046  3.5087245  2.5853418  3.1671978  5.9683110
YAB1   8.57037535 10.70713708 10.7070353  8.5703754  9.8500447  7.1994366
YAB2  53.27096930 54.68724109 54.4284068 52.1369215 53.7358663 54.5156723
YAB3   1.64307480  2.27349166  3.0010425  1.6430748  2.1711209  3.8354908
YAB4   0.93073823  0.75496556  0.9307382  1.6754800  0.9155919  2.0269187
YAB5   1.79037148  1.87840385  2.8761107  1.7903715  2.1658297  2.8807618
YAB6   1.58852915  1.41627949  1.9834491  1.6443917  1.5904213  2.2225451
YAB7   2.98751826  2.75541598  4.0673624  2.8001476  3.0138617  4.0505163
YAB8   1.59886537  1.63856327  0.6526522  0.7004366  2.5103844  0.7218423
YAB9   1.82402405  1.73629494  2.9786076  1.8240240  1.9264377  7.5924188
YAB10  0.25387047  0.25387047  0.2538705  2.0162514  1.0321389  0.5031889
YAB11  2.62445201  2.62468833  2.6244520  3.3653055  2.8741078  2.7118806
YAB12  0.61364395  0.63009457  0.6464594  0.7666961  0.6783314  0.8298088
YAI1   0.84038360  0.65794982  2.4409748  0.8403836  1.1291816  6.3243294
YAI2   1.84706443  1.84692642  1.8470644  2.5850523  2.0289561  1.4927687
YAI3   2.46630104  2.73506357  1.7091554  1.6338435  2.7354415  2.4122913
YAI4   4.17243587  3.90943669  4.0185403  4.3598451  4.1138835  2.0784002
YAI5   0.79843574  1.08460772  1.0845339  1.1751358  1.1500846  0.9661282
YAI6   0.81682199  0.44234378  4.6295839  1.9245221  3.2872842  1.9944716
YAI7   1.88362389  5.42176745  5.4217973  3.3847504  4.4034704  3.9050570
YAI8   1.56600461  1.75939237  1.5660046  0.5173834  1.3794358  3.2372622
YAI9   5.50159241  6.12078892  9.0015924  5.5015924  7.2815951  6.0416040
YAI10  2.28432579  2.72782233  7.2439705  3.8545873  5.6000909  6.6909893
YAI11  1.53760361  3.63482919  3.5435294  1.5376036  2.8580679  2.0250677
YAI12  1.53626791  1.74543256  2.5933111  1.4435320  1.5757490  1.5739083
YAI13 17.90825719 13.41583616  2.6542728  2.1226881  1.9267821 18.3876333
YAI14  4.55571912 16.14304858 16.1427115 12.6595897 14.6280621 11.7847167
YAI15  3.42245954  3.14626860  1.5676208  3.4224595  2.4759230  5.0186980
YAI16  0.67056431  2.07362376  3.0566182  0.8713338  1.4797262  2.6493489
YAI17  1.69685836  1.27346296  1.2732801  1.6968584  0.9225801  1.8607589
YAI18  4.07161189  4.50073441  4.0716119  2.9454867  4.0627721  4.9332227
YAI19 44.03458333 44.03456109 44.0345833 42.9200139 43.3436506 44.0390639
YAI20  4.21540729  4.32174496  4.2154073  3.6343806  3.8946519  4.8590087
YAI21  2.27016299  2.32372771  8.2290301  4.8541543  6.6341227  3.4023960
YAI22 12.74831543 14.06783534 14.0679075 12.7483154 13.2709173 12.8550545
YAI23  1.04802743  1.01808062  1.0112591  1.1989196  1.0408049  0.9967423
YAI24  7.80688378  4.25960550 10.7834747  7.8068838  9.4208195  9.1628326
YAI25  1.36335131  3.37963810  1.3633513  2.4285612  1.9314515  1.9435905
YAI26  2.90684275  1.41232459  3.1464454  3.0722157  2.5926588  3.2045041
YAI27  4.82774274  4.04034060  3.3165831  2.4508170  2.6292081  2.9959041
YAI28  2.81591360  2.60940689  0.8899578  2.8159136  1.2677723  0.9817989
YAI29  2.73203531  2.52163607  4.5003969  2.7320353  3.4704948  5.0135023
YAI30  2.70743534  1.98713585  0.8006466  2.7074353  1.2919824  8.2687936
YAI31  1.93668578  1.93658045  1.9366858  1.0538813  1.1340969  1.5621041
YAI32  1.64102564  1.64102563  1.6410256  2.8974359  2.1942959  1.6487552
YAI33  0.82972321  0.81973114  2.6306955  3.4546695  1.0279601  2.4735900
YAI34  2.64331541  4.93253399  4.9013799  2.6433154  3.9400377  4.4585051
YAI35  2.04506821  2.04508521  1.8968284  1.7087096  1.7703051  1.8319634
YAG1   2.54933692  3.93993558  6.0493369  2.5493369  4.4394260  2.1802143
YAG2   2.25948229  2.25956650  2.2594823  0.3423751  1.4528729  0.4920220
YAG3   0.98960446  1.00076226  7.1574604  3.8465766  5.4880636  4.4066140
YAG4   1.07910908  0.87360541  1.0791091  1.8688676  1.5607948  5.0775259
YAG5   1.09289617  1.09324964  5.6830601  2.1830601  3.9854571  4.5637290
YAG6   4.47729529  4.74161597  4.4772953  2.2487593  3.3830335  0.9751704
YAG7   2.91200265  0.90399103  0.6691450  0.6301115  0.7875174 20.7071306
YAG8   5.98821568  4.11857241  4.1184296  3.0727506  3.9478542  4.6982776
YAG9   4.76736975  2.47961651  2.4795082  1.9057377  2.4792548  5.7633668
YAG10  0.85157842  3.77163176  3.7715222  0.8515784  2.1833841  2.5241895
YAG11  3.48670255  3.87732073  6.9867025  3.4867025  5.2700112  4.7053767
YAG12  1.57899998  3.74259388  3.7425069  1.5790000  2.9434567  1.8209721
YAG13  4.55048752  4.67900184  7.6195488  4.5504875  6.0815371  8.4662144
YAG14  0.97375938  0.97374287  0.6249995  0.6290548  1.6335376  0.6248552
YAG15  2.84432185  3.61770430  4.9858761  2.8443219  4.0340822  6.1942836
YAG16  3.90624211  4.47082581  7.3520732  3.9062421  5.7936672  5.2404266
YAG17  2.33788465  2.33795639  2.3378847  1.3403135  1.7135377  3.8010003
YAG18  2.77006853  8.15865543  8.1585341  5.3771067  6.8449620  8.0208755
YAG19  6.49027424  5.50917632 10.2331080  7.1043093  8.6425883  9.9985294
YAG20  0.86339916  0.98251744  5.4048706  1.9815194  3.7120204  2.5923921
YAG21  2.99541982  3.69578504  5.7386631  2.9954198  4.5137038  3.3003579
YAG22  0.59876543  1.05473947  3.9753086  0.5987654  2.2399980  2.0058321
YAG23  0.56262386  0.60126910  3.4708680  0.5626239  1.6985848  2.6987378
YAG24  2.08003772  2.26928289  5.3283782  1.8478986  3.5530722  4.4606705
YAG25  1.87950000  3.08035277  5.3146852  1.8795000  3.6864128  0.9465887
YAG26  0.62414781  0.65390173  5.0069444  1.6527778  3.3227839  3.9442891
YAG27  3.09992000  2.31252467  6.5999200  3.0999200  4.9475728  1.0730897
YAG28  0.86030991  0.88503436  4.2882126  0.8603099  2.6021672  4.2176147
YAG29  0.07074949  0.72735092  6.0100303  2.5100303  4.3715168  2.2355695
YAG30  0.46669000  1.54732972  7.3499300  3.8499300  5.6875926  2.3848806
YAC1   1.40139123  2.27678150  4.9013912  1.4013912  3.2377302  0.2441322
YAC2   1.64788713  3.20306204  4.5601376  1.6478871  3.2896412  3.5861285
YAC3   0.72655978  0.82264941  6.1185606  2.6185606  4.3172360  6.4087791
YAC4   1.09723495  0.86703152  5.8233514  2.3695976  4.1916317  0.6483775
YAC5   2.93115557  3.94951167  5.7995318  2.9311556  4.5297922  2.5320095
YAC6   0.54893870  0.48753454  0.5489387  1.2278225  0.7583333  0.5528410
YAC7   1.86323404  3.06635102  3.9520638  1.8632340  3.1546103  3.1812793
YAC8   1.25783550  0.65667255  7.2033890  4.7683241  5.9336542  6.3506597
YAC9   0.87350898  0.97202279  5.3971497  2.1095250  3.7566096  1.5837057
YAC10  2.58773523  4.61761196  4.6175333  2.5877352  3.8742645  1.2087104
YAC11  6.84463515  7.97419436 10.3446352  6.8446352  8.7810648  8.3544001
YAC12  1.82866492  2.22982145  5.3286649  1.8286649  3.6183147  2.6163645
YAC13  5.68734181  4.50676209  5.6873418  4.0336516  5.2182008  7.6347268
YAC14  2.57222049  2.13714471  2.1371447  1.3277470  1.8649361  3.1808405
YAC15  3.86759191  3.86729179  9.1831685  5.6831685  7.4389747  6.2728353
YAC16  0.90349483  1.18178224  0.9034948  0.7867049  0.9457474  2.0424156
YAC17  5.26498644  5.80308181  7.0853978  5.2649864  6.4634574  8.6913124
YAC18  1.87279661  1.64035878  5.3727966  1.8727966  3.6768294  2.5083515
YAC19  0.84371342  2.30643885  2.2918438  0.8437134  1.6132961  1.3512068
YAC20  0.38731474  0.09952735  3.4110916  0.1356388  1.7091136  2.4695118
YAC21  1.95227324  1.86819987  5.0995297  1.9522732  3.4146410  4.6145942
YAC22  2.71347047  2.64481865  8.1040215  4.6040215  6.3975309  5.5854955
YAC23  1.80620861  1.10672591  4.9005795  1.8062086  3.2294536  4.9645001
YAC24  1.30648607  2.96986108  2.9697456  0.4649762  2.0995904  0.9283821
YAC25  2.96701565  2.85465812  7.7948624  4.2948624  6.0634344  5.1157282
YAC26  4.42214970  7.35639284  7.3562814  4.4221497  6.1816126  1.1124711
YAC27  0.99068519  0.74770121  5.5295741  2.2925370  3.8911075  2.3476266
YAC28  3.47254800  3.78016924  6.6161036  3.4725480  4.8511688  6.2423362
YAC29  1.08984505  3.14643861  3.1464601  1.0898451  1.7003076  3.0929558
YAD1   5.32880508  5.32899343  4.1338865  4.3937118  5.6129407  5.5595531
YAD2   4.16840894  4.15583328  5.9936273  2.9568189  4.4446085  5.7430167
YAD3   0.42340177  0.77174669  0.4314063  0.5811338  0.3718245  1.5616759
YAD4   1.74576093  1.74547087  0.8071617  0.2615587  1.0219153  1.9092131
YAD5   1.01524242  1.77444600  1.0152424  1.2161994  1.9261107  3.2037313
YAD6   0.97887135  0.96238162  2.2619400  2.6515504  1.0119491  0.6661060
YAD7   0.93418975  0.80119406  2.2267709  2.5916119  0.9727596  0.5569037
YAD8   0.95015958  0.89533123  2.2338180  2.6090432  0.9862256  0.6025845
YAD9   1.60601348  1.72683440  0.7662312  0.9544032  1.9282141  2.6459214
YAD10  1.79944413  1.80838059  0.9992112  1.2296460  1.9809520  2.5535343
YAD11  3.63702912  3.63726892  2.8391202  2.3543440  3.9637990  2.9559647
YAD12  0.89467778  0.94672217  0.8946778  1.3219889  0.4582498  0.8073852
YAD13  1.02927451  0.82352941  1.0292745  1.1910392  0.8124387  0.8851213
YAD14  1.70683124  2.96006979  3.0763781  3.2308297  3.0296397  1.5749024
YAD15  9.08651852  9.08666668  9.0865185  7.1420741  8.0755267  9.1451860
YAD16  0.41025641  0.41025641  1.0255179  1.8332103  0.4145299  0.4087326
YAD17  8.25973952  6.53546777  6.3776383  5.9265859  6.2885599  7.0287042
YAD18  7.23138746  6.65853431  6.5105897  6.8439231  6.8157312  6.9441209
YAD19  5.55066667  5.55673526  5.0425139  5.0911023  5.7691484  5.1836609
YAD20  1.54227823  8.52836495  8.5281653  5.0563911  6.9132895  6.9077093
YAD21  1.41039755  1.45990904  2.5926606  0.9073394  0.7864160  1.6406287
YAD22  2.55734886  1.55287633  1.4130735  0.9306174  1.5983157  2.5762868
YAD23  2.74067749  1.60152285  1.4588519  0.9561418  1.6396497  0.9762310
YAD24  0.55143439  1.17437947  0.5514344  0.6494659  0.7257569  1.3104961
YAD25  1.47668822  1.46966525  3.3810704  0.4404813  1.5987701  1.5847387
YAD26  0.56735469  1.20168108  0.5673547  0.6549806  0.7623183  1.5479484
YAD27  4.58130172  3.02046450  3.0202983  1.8067608  2.7016179 16.4415476
YAD28  6.55007236  5.16689524  5.1667519  4.2536441  4.8230043  5.0146430
YAD29  1.44673203  0.98500034  1.1459238  1.1694246  0.9875650  1.3370715
YAD30  3.92046205  3.91847882  3.9204620  3.3983498  3.5601419  3.6604391

$ARIMA
                             YAF2                              YAF3 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,1) with drift" 
                             YAF4                              YAF5 
        "ARIMA(0,1,2) with drift"         "ARIMA(1,1,0) with drift" 
                             YAF6                              YAF7 
        "ARIMA(0,1,1) with drift"         "ARIMA(1,1,0) with drift" 
                             YAF8                              YAF9 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAF10                             YAF11 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAF12                             YAF13 
                   "ARIMA(0,2,1)"                    "ARIMA(0,2,1)" 
                            YAF14                             YAF15 
                   "ARIMA(2,2,0)"         "ARIMA(0,1,0) with drift" 
                            YAF16                             YAF17 
                   "ARIMA(0,2,0)"         "ARIMA(0,1,0) with drift" 
                             YAM1                              YAM2 
                   "ARIMA(0,1,0)"         "ARIMA(0,1,1) with drift" 
                             YAM3                              YAM4 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,1,0)" 
                             YAM5                              YAM6 
                   "ARIMA(0,1,1)"         "ARIMA(0,1,0) with drift" 
                             YAM7                              YAM8 
                   "ARIMA(0,2,0)" "ARIMA(0,0,0) with non-zero mean" 
                            YAM10                             YAM11 
"ARIMA(2,0,0) with non-zero mean" "ARIMA(1,0,0) with non-zero mean" 
                            YAM12                             YAM13 
"ARIMA(0,0,1) with non-zero mean" "ARIMA(0,0,0) with non-zero mean" 
                            YAM14                             YAM15 
                   "ARIMA(0,1,0)"                    "ARIMA(0,1,0)" 
                            YAM16                             YAM17 
                   "ARIMA(0,1,0)"                    "ARIMA(0,1,0)" 
                            YAM18                             YAM19 
        "ARIMA(0,1,0) with drift" "ARIMA(2,0,1) with non-zero mean" 
                            YAM20                             YAM21 
                   "ARIMA(0,1,0)" "ARIMA(2,0,0) with non-zero mean" 
                            YAM22                             YAM23 
"ARIMA(2,0,0) with non-zero mean"                    "ARIMA(0,2,1)" 
                            YAM24                             YAM25 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAM26                             YAM27 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,2,1)" 
                            YAM28                             YAM29 
                   "ARIMA(0,2,1)" "ARIMA(1,0,0) with non-zero mean" 
                            YAM30                              YAB1 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                             YAB2                              YAB3 
                   "ARIMA(1,1,0)"         "ARIMA(0,1,0) with drift" 
                             YAB4                              YAB5 
                   "ARIMA(0,1,0)"         "ARIMA(0,1,0) with drift" 
                             YAB6                              YAB7 
        "ARIMA(0,1,2) with drift"                    "ARIMA(0,2,0)" 
                             YAB8                              YAB9 
"ARIMA(0,0,0) with non-zero mean"         "ARIMA(0,1,0) with drift" 
                            YAB10                             YAB11 
                   "ARIMA(0,1,0)"                    "ARIMA(0,1,0)" 
                            YAB12                              YAI1 
                   "ARIMA(2,1,0)"         "ARIMA(0,1,0) with drift" 
                             YAI2                              YAI3 
                   "ARIMA(0,1,0)" "ARIMA(0,0,1) with non-zero mean" 
                             YAI4                              YAI5 
                   "ARIMA(1,1,0)" "ARIMA(1,0,0) with non-zero mean" 
                             YAI6                              YAI7 
                   "ARIMA(0,2,1)"                    "ARIMA(0,2,1)" 
                             YAI8                              YAI9 
                   "ARIMA(0,1,0)"         "ARIMA(0,1,0) with drift" 
                            YAI10                             YAI11 
                   "ARIMA(0,2,1)"         "ARIMA(0,1,0) with drift" 
                            YAI12                             YAI13 
                   "ARIMA(0,2,0)"                    "ARIMA(0,2,0)" 
                            YAI14                             YAI15 
                   "ARIMA(0,2,0)"         "ARIMA(0,1,0) with drift" 
                            YAI16                             YAI17 
        "ARIMA(0,1,1) with drift"         "ARIMA(0,1,0) with drift" 
                            YAI18                             YAI19 
                   "ARIMA(0,1,0)"                    "ARIMA(0,1,0)" 
                            YAI20                             YAI21 
                   "ARIMA(0,1,0)"                    "ARIMA(0,2,1)" 
                            YAI22                             YAI23 
        "ARIMA(0,1,0) with drift" "ARIMA(0,0,1) with non-zero mean" 
                            YAI24                             YAI25 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,1,0)" 
                            YAI26                             YAI27 
"ARIMA(1,0,0) with non-zero mean"                    "ARIMA(1,2,0)" 
                            YAI28                             YAI29 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAI30                             YAI31 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,1,0)" 
                            YAI32                             YAI33 
                   "ARIMA(0,1,0)" "ARIMA(0,0,0) with non-zero mean" 
                            YAI34                             YAI35 
        "ARIMA(0,1,0) with drift" "ARIMA(0,0,0) with non-zero mean" 
                             YAG1                              YAG2 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,1,0)" 
                             YAG3                              YAG4 
                   "ARIMA(1,2,0)"                    "ARIMA(0,1,0)" 
                             YAG5                              YAG6 
                   "ARIMA(0,2,0)"                    "ARIMA(0,1,0)" 
                             YAG7                              YAG8 
"ARIMA(1,0,0) with non-zero mean" "ARIMA(2,0,0) with non-zero mean" 
                             YAG9                             YAG10 
"ARIMA(2,0,0) with non-zero mean"         "ARIMA(0,1,0) with drift" 
                            YAG11                             YAG12 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAG13                             YAG14 
        "ARIMA(0,1,0) with drift" "ARIMA(0,0,0) with non-zero mean" 
                            YAG15                             YAG16 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAG17                             YAG18 
                   "ARIMA(0,1,0)"                    "ARIMA(0,2,0)" 
                            YAG19                             YAG20 
                   "ARIMA(0,2,0)"                    "ARIMA(0,2,1)" 
                            YAG21                             YAG22 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAG23                             YAG24 
        "ARIMA(0,1,0) with drift"                    "ARIMA(3,2,0)" 
                            YAG25                             YAG26 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,2,1)" 
                            YAG27                             YAG28 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAG29                             YAG30 
                   "ARIMA(0,2,0)"                    "ARIMA(0,2,0)" 
                             YAC1                              YAC2 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                             YAC3                              YAC4 
                   "ARIMA(0,2,1)"                    "ARIMA(1,2,0)" 
                             YAC5                              YAC6 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,1,0)" 
                             YAC7                              YAC8 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,2,0)" 
                             YAC9                             YAC10 
                   "ARIMA(0,2,0)"         "ARIMA(0,1,0) with drift" 
                            YAC11                             YAC12 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAC13                             YAC14 
                   "ARIMA(0,1,0)"                    "ARIMA(2,1,0)" 
                            YAC15                             YAC16 
                   "ARIMA(0,2,0)"                    "ARIMA(0,1,0)" 
                            YAC17                             YAC18 
        "ARIMA(0,1,0) with drift"         "ARIMA(0,1,0) with drift" 
                            YAC19                             YAC20 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,2,0)" 
                            YAC21                             YAC22 
        "ARIMA(0,1,0) with drift"                    "ARIMA(0,2,1)" 
                            YAC23                             YAC24 
        "ARIMA(0,1,0) with drift"                    "ARIMA(1,1,0)" 
                            YAC25                             YAC26 
                   "ARIMA(0,2,0)"         "ARIMA(0,1,0) with drift" 
                            YAC27                             YAC28 
                   "ARIMA(0,2,0)"         "ARIMA(0,1,0) with drift" 
                            YAC29                              YAD1 
        "ARIMA(0,1,0) with drift" "ARIMA(0,0,0) with non-zero mean" 
                             YAD2                              YAD3 
                   "ARIMA(0,2,1)"         "ARIMA(0,1,1) with drift" 
                             YAD4                              YAD5 
"ARIMA(0,0,0) with non-zero mean"                    "ARIMA(0,1,0)" 
                             YAD6                              YAD7 
                   "ARIMA(0,1,1)"                    "ARIMA(0,1,1)" 
                             YAD8                              YAD9 
                   "ARIMA(0,1,1)" "ARIMA(1,0,1) with non-zero mean" 
                            YAD10                             YAD11 
"ARIMA(0,0,1) with non-zero mean" "ARIMA(0,0,0) with non-zero mean" 
                            YAD12                             YAD13 
                   "ARIMA(0,1,0)"                    "ARIMA(0,1,0)" 
                            YAD14                             YAD15 
"ARIMA(1,0,0) with non-zero mean"                    "ARIMA(0,1,0)" 
                            YAD16                             YAD17 
"ARIMA(0,0,0) with non-zero mean" "ARIMA(1,0,0) with non-zero mean" 
                            YAD18                             YAD19 
"ARIMA(0,0,0) with non-zero mean" "ARIMA(0,0,1) with non-zero mean" 
                            YAD20                             YAD21 
                   "ARIMA(0,2,0)"                    "ARIMA(0,2,0)" 
                            YAD22                             YAD23 
"ARIMA(1,0,0) with non-zero mean" "ARIMA(0,0,1) with non-zero mean" 
                            YAD24                             YAD25 
                   "ARIMA(0,1,0)"                    "ARIMA(0,2,0)" 
                            YAD26                             YAD27 
                   "ARIMA(0,1,0)" "ARIMA(1,0,0) with non-zero mean" 
                            YAD28                             YAD29 
"ARIMA(1,0,0) with non-zero mean" "ARIMA(0,0,1) with non-zero mean" 
                            YAD30 
                   "ARIMA(0,1,0)"

$ETS
         YAF2          YAF3          YAF4          YAF5          YAF6 
 "ETS(A,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)" 
         YAF7          YAF8          YAF9         YAF10         YAF11 
 "ETS(M,A,N)"  "ETS(M,N,N)"  "ETS(A,N,N)"  "ETS(M,N,N)"  "ETS(M,A,N)" 
        YAF12         YAF13         YAF14         YAF15         YAF16 
 "ETS(A,A,N)"  "ETS(A,A,N)"  "ETS(M,A,N)"  "ETS(A,A,N)"  "ETS(M,N,N)" 
        YAF17          YAM1          YAM2          YAM3          YAM4 
 "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(M,A,N)" "ETS(A,Ad,N)"  "ETS(A,N,N)" 
         YAM5          YAM6          YAM7          YAM8         YAM10 
 "ETS(M,N,N)"  "ETS(M,A,N)"  "ETS(A,A,N)"  "ETS(A,N,N)"  "ETS(M,A,N)" 
        YAM11         YAM12         YAM13         YAM14         YAM15 
 "ETS(M,N,N)"  "ETS(M,N,N)"  "ETS(M,N,N)"  "ETS(A,N,N)"  "ETS(M,N,N)" 
        YAM16         YAM17         YAM18         YAM19         YAM20 
 "ETS(M,N,N)"  "ETS(M,N,N)"  "ETS(A,A,N)"  "ETS(A,N,N)"  "ETS(A,N,N)" 
        YAM21         YAM22         YAM23         YAM24         YAM25 
 "ETS(A,N,N)"  "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)" 
        YAM26         YAM27         YAM28         YAM29         YAM30 
 "ETS(M,N,N)"  "ETS(A,A,N)"  "ETS(M,A,N)"  "ETS(M,N,N)"  "ETS(M,A,N)" 
         YAB1          YAB2          YAB3          YAB4          YAB5 
 "ETS(A,N,N)"  "ETS(M,N,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(A,A,N)" 
         YAB6          YAB7          YAB8          YAB9         YAB10 
 "ETS(M,A,N)"  "ETS(A,A,N)"  "ETS(M,N,N)"  "ETS(A,A,N)"  "ETS(A,N,N)" 
        YAB11         YAB12          YAI1          YAI2          YAI3 
 "ETS(A,N,N)"  "ETS(A,A,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(M,N,N)" 
         YAI4          YAI5          YAI6          YAI7          YAI8 
 "ETS(M,N,N)"  "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(M,N,N)"  "ETS(A,N,N)" 
         YAI9         YAI10         YAI11         YAI12         YAI13 
 "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(A,A,N)"  "ETS(M,A,N)" 
        YAI14         YAI15         YAI16         YAI17         YAI18 
 "ETS(M,N,N)"  "ETS(A,A,N)"  "ETS(A,A,N)"  "ETS(M,N,N)"  "ETS(M,N,N)" 
        YAI19         YAI20         YAI21         YAI22         YAI23 
 "ETS(A,N,N)"  "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(A,N,N)" 
        YAI24         YAI25         YAI26         YAI27         YAI28 
 "ETS(A,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(A,A,N)"  "ETS(A,A,N)" 
        YAI29         YAI30         YAI31         YAI32         YAI33 
 "ETS(M,A,N)"  "ETS(A,A,N)"  "ETS(A,N,N)"  "ETS(A,N,N)"  "ETS(A,N,N)" 
        YAI34         YAI35          YAG1          YAG2          YAG3 
 "ETS(A,N,N)"  "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(A,A,N)" 
         YAG4          YAG5          YAG6          YAG7          YAG8 
 "ETS(M,N,N)"  "ETS(A,A,N)"  "ETS(M,N,N)"  "ETS(M,N,N)"  "ETS(A,N,N)" 
         YAG9         YAG10         YAG11         YAG12         YAG13 
 "ETS(A,N,N)"  "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(M,A,N)" 
        YAG14         YAG15         YAG16         YAG17         YAG18 
 "ETS(M,N,N)"  "ETS(A,A,N)"  "ETS(A,A,N)"  "ETS(M,N,N)"  "ETS(M,N,N)" 
        YAG19         YAG20         YAG21         YAG22         YAG23 
 "ETS(A,A,N)"  "ETS(A,A,N)"  "ETS(A,A,N)"  "ETS(A,A,N)"  "ETS(M,A,N)" 
        YAG24         YAG25         YAG26         YAG27         YAG28 
 "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(A,A,N)" 
        YAG29         YAG30          YAC1          YAC2          YAC3 
 "ETS(M,A,N)"  "ETS(A,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)" 
         YAC4          YAC5          YAC6          YAC7          YAC8 
 "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(A,A,N)"  "ETS(A,A,N)" 
         YAC9         YAC10         YAC11         YAC12         YAC13 
 "ETS(A,A,N)"  "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(A,A,N)" 
        YAC14         YAC15         YAC16         YAC17         YAC18 
 "ETS(A,N,N)"  "ETS(A,A,N)"  "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(M,A,N)" 
        YAC19         YAC20         YAC21         YAC22         YAC23 
 "ETS(M,N,N)"  "ETS(M,A,N)"  "ETS(A,A,N)"  "ETS(M,A,N)"  "ETS(M,A,N)" 
        YAC24         YAC25         YAC26         YAC27         YAC28 
 "ETS(A,N,N)"  "ETS(M,A,N)"  "ETS(A,N,N)"  "ETS(A,A,N)"  "ETS(M,A,N)" 
        YAC29          YAD1          YAD2          YAD3          YAD4 
 "ETS(A,N,N)"  "ETS(A,N,N)" "ETS(M,Ad,N)" "ETS(A,Ad,N)"  "ETS(M,N,N)" 
         YAD5          YAD6          YAD7          YAD8          YAD9 
 "ETS(A,N,N)"  "ETS(M,N,N)"  "ETS(M,A,N)"  "ETS(M,A,N)"  "ETS(A,N,N)" 
        YAD10         YAD11         YAD12         YAD13         YAD14 
 "ETS(A,N,N)"  "ETS(A,N,N)"  "ETS(M,N,N)"  "ETS(M,N,N)"  "ETS(A,N,N)" 
        YAD15         YAD16         YAD17         YAD18         YAD19 
 "ETS(A,N,N)"  "ETS(M,N,N)"  "ETS(A,N,N)"  "ETS(A,N,N)"  "ETS(M,N,N)" 
        YAD20         YAD21         YAD22         YAD23         YAD24 
 "ETS(M,N,N)"  "ETS(M,A,N)"  "ETS(M,N,N)"  "ETS(M,N,N)"  "ETS(A,N,N)" 
        YAD25         YAD26         YAD27         YAD28         YAD29 
 "ETS(M,A,N)"  "ETS(M,N,N)"  "ETS(A,N,N)"  "ETS(M,N,N)"  "ETS(M,N,N)" 
        YAD30 
 "ETS(A,N,N)"

$forecasts
$forecasts$arima
         YAF2     YAF3     YAF4     YAF5     YAF6     YAF7      YAF8     YAF9
[1,] 579581.0 390955.9 369704.9 326878.3 21141635 15770.87  904964.3 673803.7
[2,] 605761.9 407325.1 392255.0 366064.9 21677177 16255.32  962222.7 709311.4
[3,] 631942.9 423694.4 408717.0 365288.0 22212720 16905.57 1019481.0 744819.1
[4,] 658123.8 440063.6 425179.1 390109.0 22748262 17466.14 1076739.3 780326.8
[5,] 684304.8 456432.8 441641.1 398533.7 23283804 18075.21 1133997.7 815834.5
[6,] 710485.7 472802.0 458103.2 417460.7 23819346 18658.05 1191256.0 851342.2
         YAF10 YAF11     YAF12   YAF13    YAF14     YAF15  YAF16    YAF17  YAM1
[1,]  906621.4 55.13  8963.293 1904976 54652.02  908663.9 1068.0 8.764489 71755
[2,]  951113.7 56.33  9479.587 2098112 52595.04  950829.8 1094.1 8.945009 71755
[3,]  995606.1 57.53  9995.880 2291249 54523.59  992995.7 1120.2 9.125528 71755
[4,] 1040098.5 58.73 10512.173 2484385 56366.94 1035161.6 1146.3 9.306048 71755
[5,] 1084590.9 59.93 11028.467 2677521 55539.93 1077327.5 1172.4 9.486567 71755
[6,] 1129083.2 61.13 11544.760 2870657 57751.48 1119493.4 1198.5 9.667087 71755
         YAM2     YAM3  YAM4     YAM5     YAM6   YAM7     YAM8     YAM10
[1,] 635257.8 7089.829 18139 28.87587 2.753552 1774.8 94.18462  70.59584
[2,] 665525.9 7323.188 18139 28.87587 2.766793 1630.2 94.18462  92.62441
[3,] 695794.0 7556.547 18139 28.87587 2.780035 1485.6 94.18462 116.32355
[4,] 726062.0 7789.906 18139 28.87587 2.793276 1341.0 94.18462 135.51812
[5,] 756330.1 8023.265 18139 28.87587 2.806518 1196.4 94.18462 146.59663
[6,] 786598.2 8256.624 18139 28.87587 2.819759 1051.8 94.18462 148.78354
        YAM11    YAM12    YAM13 YAM14 YAM15 YAM16 YAM17    YAM18     YAM19
[1,] 19717359 12630014 2725.212   811   770 100.8   175 5773.286  99.55630
[2,] 19172800 12247801 2725.212   811   770 100.8   175 5964.571  95.03239
[3,] 18805626 12247801 2725.212   811   770 100.8   175 6155.857  95.95622
[4,] 18558055 12247801 2725.212   811   770 100.8   175 6347.143 100.24116
[5,] 18391128 12247801 2725.212   811   770 100.8   175 6538.429 100.11698
[6,] 18278576 12247801 2725.212   811   770 100.8   175 6729.714  96.18441
     YAM20    YAM21    YAM22    YAM23    YAM24   YAM25   YAM26    YAM27
[1,]  9383 205.5751 95.59372 12671.75  9352.15 11898.3 25885.5 610.7561
[2,]  9383 188.8118 88.46585 13290.51  9654.30 12170.6 26363.0 662.5122
[3,]  9383 177.4192 85.72708 13909.26  9956.45 12442.9 26840.5 714.2684
[4,]  9383 180.7550 86.55871 14528.01 10258.60 12715.2 27318.0 766.0245
[5,]  9383 191.6987 88.42534 15146.77 10560.75 12987.5 27795.5 817.7806
[6,]  9383 197.8305 89.59875 15765.52 10862.90 13259.8 28273.0 869.5367
        YAM28    YAM29    YAM30     YAB1     YAB2     YAB3  YAB4     YAB5
[1,] 1318.168 7873.221 76266.65 31148.35 7935.886 621170.9 80389 10547.31
[2,] 1417.335 7736.379 77866.30 32487.70 8124.539 653863.9 80389 10909.63
[3,] 1516.503 7620.631 79465.96 33827.05 8217.978 686556.8 80389 11271.94
[4,] 1615.671 7522.726 81065.61 35166.40 8264.259 719249.8 80389 11634.25
[5,] 1714.838 7439.912 82665.26 36505.75 8287.182 751942.7 80389 11996.56
[6,] 1814.006 7369.864 84264.91 37845.10 8298.536 784635.7 80389 12358.88
         YAB6   YAB7     YAB8     YAB9 YAB10  YAB11    YAB12     YAI1  YAI2
[1,] 834.7073 721910 169402.1 250283.4 39098 142157 26748.39 1257.088 39177
[2,] 800.3679 751718 169402.1 270777.7 39098 142157 26454.84 1323.176 39177
[3,] 815.7275 781526 169402.1 291272.1 39098 142157 26733.55 1389.265 39177
[4,] 831.0871 811334 169402.1 311766.5 39098 142157 26638.23 1455.353 39177
[5,] 846.4467 841142 169402.1 332260.8 39098 142157 26596.86 1521.441 39177
[6,] 861.8063 870950 169402.1 352755.2 39098 142157 26668.63 1587.529 39177
         YAI3     YAI4     YAI5    YAI6     YAI7   YAI8  YAI9    YAI10    YAI11
[1,] 378.1661 3055.081 697.5569 1938336 22644175 8800.8 290.2 219836.9 662.7529
[2,] 235.6548 3024.749 650.2141 2016812 23488151 8800.8 310.4 227533.8 692.9059
[3,] 235.6548 3036.532 611.8632 2095289 24332126 8800.8 330.6 235230.7 723.0588
[4,] 235.6548 3031.955 580.7964 2173765 25176102 8800.8 350.8 242927.6 753.2118
[5,] 235.6548 3033.733 555.6301 2252241 26020077 8800.8 371.0 250624.5 783.3647
[6,] 235.6548 3033.042 535.2438 2330717 26864053 8800.8 391.2 258321.4 813.5176
      YAI12  YAI13  YAI14    YAI15    YAI16    YAI17 YAI18 YAI19  YAI20
[1,] 1524.9 1372.3 1014.2 260.4941 139.2705 1332.518 111.5  38.2 13.936
[2,] 1577.6 1706.2 1218.3 273.8882 146.8112 1392.835 111.5  38.2 13.936
[3,] 1630.3 2040.1 1422.4 287.2824 154.3520 1453.153 111.5  38.2 13.936
[4,] 1683.0 2374.0 1626.5 300.6765 161.8928 1513.471 111.5  38.2 13.936
[5,] 1735.7 2707.9 1830.6 314.0706 169.4335 1573.788 111.5  38.2 13.936
[6,] 1788.4 3041.8 2034.7 327.4647 176.9743 1634.106 111.5  38.2 13.936
        YAI21    YAI22    YAI23  YAI24 YAI25    YAI26    YAI27    YAI28
[1,] 1318.168 3205.167 23.00821 135512  56.8 489.3039 4607.910 388.0684
[2,] 1417.335 3293.935 23.29348 139830  56.8 499.4178 4816.082 404.4368
[3,] 1516.503 3382.702 23.29348 144148  56.8 504.7168 5515.399 420.8053
[4,] 1615.671 3471.470 23.29348 148466  56.8 507.4931 5783.759 437.1737
[5,] 1714.838 3560.237 23.29348 152784  56.8 508.9477 6430.265 453.5421
[6,] 1814.006 3649.005 23.29348 157102  56.8 509.7098 6744.964 469.9105
        YAI29  YAI30 YAI31 YAI32    YAI33 YAI34    YAI35     YAG1  YAG2
[1,] 150.4105 17.555  6.38  14.2 7.875385  3.46 2.799167 245.9575 52.52
[2,] 156.2211 18.770  6.38  14.2 7.875385  3.58 2.799167 254.3150 52.52
[3,] 162.0316 19.985  6.38  14.2 7.875385  3.70 2.799167 262.6725 52.52
[4,] 167.8421 21.200  6.38  14.2 7.875385  3.82 2.799167 271.0300 52.52
[5,] 173.6526 22.415  6.38  14.2 7.875385  3.94 2.799167 279.3875 52.52
[6,] 179.4632 23.630  6.38  14.2 7.875385  4.06 2.799167 287.7450 52.52
          YAG3  YAG4 YAG5   YAG6      YAG7     YAG8      YAG9     YAG10
[1,]  92.61077 11.39  120 107.69 105.60777 186.5144 124.34173  95.52632
[2,] 100.08035 11.39  125 107.69  99.73331 179.1672 118.24181  98.65263
[3,] 107.83204 11.39  130 107.69  96.70411 170.5083 111.05919 101.77895
[4,] 115.41833 11.39  135 107.69  95.14210 162.2249 104.63702 104.90526
[5,] 123.10159 11.39  140 107.69  94.33663 154.8605  99.74308 108.03158
[6,] 130.72801 11.39  145 107.69  93.92129 148.5141  96.47931 111.15789
        YAG11    YAG12    YAG13    YAG14    YAG15    YAG16 YAG17 YAG18 YAG19
[1,] 370305.5 113285.7  97293.5 4317.462 31650.58 478816.8 41.42   666   606
[2,] 384055.0 119333.3 100636.0 4317.462 33023.17 497020.7 41.42   734   643
[3,] 397804.5 125381.0 103978.5 4317.462 34395.75 515224.5 41.42   802   680
[4,] 411554.0 131428.7 107321.0 4317.462 35768.33 533428.3 41.42   870   717
[5,] 425303.5 137476.3 110663.5 4317.462 37140.92 551632.2 41.42   938   754
[6,] 439053.0 143524.0 114006.0 4317.462 38513.50 569836.0 41.42  1006   791
        YAG20    YAG21    YAG22    YAG23    YAG24    YAG25    YAG26 YAG27
[1,] 877.1081 5.807143 10.48571 137.5071 65.17531 22.85714 11.84057  6.25
[2,] 896.1162 6.014286 10.87143 143.5143 66.95326 23.61429 12.38113  6.50
[3,] 915.1243 6.221429 11.25714 149.5214 69.61589 24.37143 12.92170  6.75
[4,] 934.1324 6.428571 11.64286 155.5286 72.06267 25.12857 13.46226  7.00
[5,] 953.1405 6.635714 12.02857 161.5357 75.01868 25.88571 14.00283  7.25
[6,] 972.1486 6.842857 12.41429 167.5429 77.38557 26.64286 14.54340  7.50
        YAG28 YAG29 YAG30    YAC1    YAC2     YAC3     YAC4      YAC5  YAC6
[1,] 7.664286   8.1   4.5 76.5825 28.6575 18.71678 24.50945  98.85917 19.84
[2,] 7.928571   8.5   4.8 78.6550 29.6650 19.73355 27.18523 102.06833 19.84
[3,] 8.192857   8.9   5.1 80.7275 30.6725 20.75033 29.70478 105.27750 19.84
[4,] 8.457143   9.3   5.4 82.8000 31.6800 21.76711 32.31954 108.48667 19.84
[5,] 8.721429   9.7   5.7 84.8725 32.6875 22.78389 34.87627 111.69583 19.84
[6,] 8.985714  10.1   6.0 86.9450 33.6950 23.80066 37.46837 114.90500 19.84
       YAC7  YAC8  YAC9    YAC10    YAC11    YAC12 YAC13    YAC14 YAC15 YAC16
[1,] 33.625 27.98 42.67 75474.42 32767.92 54381.67 40034 55177.55 58574 26875
[2,] 34.560 30.33 46.41 77166.83 33675.83 56928.33 40034 54700.53 62860 26875
[3,] 35.495 32.68 50.15 78859.25 34583.75 59475.00 40034 52430.67 67146 26875
[4,] 36.430 35.03 53.89 80551.67 35491.67 62021.67 40034 50173.72 71432 26875
[5,] 37.365 37.38 57.63 82244.08 36399.58 64568.33 40034 49314.62 75718 26875
[6,] 38.300 39.73 61.37 83936.50 37307.50 67115.00 40034 50062.03 80004 26875
       YAC17    YAC18    YAC19 YAC20    YAC21    YAC22 YAC23    YAC24 YAC25
[1,] 33610.5 54.46667 32175926  5368 2083.917 2097.978  1743 1891.306  3378
[2,] 34761.0 56.43333 32910651  5595 2150.833 2240.956  1832 1954.300  3591
[3,] 35911.5 58.40000 33645377  5822 2217.750 2383.934  1921 1999.752  3804
[4,] 37062.0 60.36667 34380103  6049 2284.667 2526.912  2010 2032.548  4017
[5,] 38212.5 62.33333 35114828  6276 2351.583 2669.890  2099 2056.211  4230
[6,] 39363.0 64.30000 35849554  6503 2418.500 2812.868  2188 2073.285  4443
         YAC26 YAC27    YAC28    YAC29     YAD1     YAD2     YAD3     YAD4 YAD5
[1,]  937.6667  1676 2406.917 2086.083 114.6364 36595.27 297.1427 1917.333  522
[2,]  984.3333  1803 2522.833 2127.167 114.6364 36690.55 298.6082 1917.333  522
[3,] 1031.0000  1930 2638.750 2168.250 114.6364 36785.82 300.0736 1917.333  522
[4,] 1077.6667  2057 2754.667 2209.333 114.6364 36881.10 301.5391 1917.333  522
[5,] 1124.3333  2184 2870.583 2250.417 114.6364 36976.37 303.0045 1917.333  522
[6,] 1171.0000  2311 2986.500 2291.500 114.6364 37071.65 304.4700 1917.333  522
         YAD6     YAD7    YAD8     YAD9    YAD10  YAD11 YAD12 YAD13    YAD14
[1,] 449.4026 445.7425 895.012 902.3788 986.8827 3597.4  37.1  39.8 1258.433
[2,] 449.4026 445.7425 895.012 890.9857 965.0326 3597.4  37.1  39.8 1411.542
[3,] 449.4026 445.7425 895.012 895.9207 965.0326 3597.4  37.1  39.8 1490.890
[4,] 449.4026 445.7425 895.012 893.7831 965.0326 3597.4  37.1  39.8 1532.012
[5,] 449.4026 445.7425 895.012 894.7090 965.0326 3597.4  37.1  39.8 1553.323
[6,] 449.4026 445.7425 895.012 894.3080 965.0326 3597.4  37.1  39.8 1564.368
     YAD15    YAD16    YAD17    YAD18   YAD19 YAD20 YAD21    YAD22    YAD23
[1,]  23.2 9.411111 403806.5 2.273333 1557784   694 26628 457.5204 441.9463
[2,]  23.2 9.411111 398773.2 2.273333 1550156   749 26815 449.3278 413.4229
[3,]  23.2 9.411111 396017.6 2.273333 1550156   804 27002 444.9918 413.4229
[4,]  23.2 9.411111 394509.0 2.273333 1550156   859 27189 442.6970 413.4229
[5,]  23.2 9.411111 393683.0 2.273333 1550156   914 27376 441.4825 413.4229
[6,]  23.2 9.411111 393230.8 2.273333 1550156   969 27563 440.8397 413.4229
      YAD24 YAD25  YAD26    YAD27    YAD28    YAD29 YAD30
[1,] 333594 28179 322404 10468.06 7937.202 55.72755  1016
[2,] 333594 28363 322404 10642.03 8030.728 55.18222  1016
[3,] 333594 28547 322404 10783.43 8106.004 55.18222  1016
[4,] 333594 28731 322404 10898.34 8166.591 55.18222  1016
[5,] 333594 28915 322404 10991.73 8215.355 55.18222  1016
[6,] 333594 29099 322404 11067.63 8254.604 55.18222  1016

$forecasts$ets
         YAF2     YAF3     YAF4     YAF5     YAF6     YAF7     YAF8     YAF9
[1,] 556280.7 384603.9 381979.7 318277.4 21230649 16129.36 847700.2 638290.3
[2,] 594333.0 385162.7 399547.7 334201.6 21690238 17323.96 847700.2 638290.3
[3,] 632385.3 385721.5 417115.8 350125.8 22149828 18518.57 847700.2 638290.3
[4,] 670437.6 386280.4 434683.8 366050.0 22609417 19713.17 847700.2 638290.3
[5,] 708489.9 386839.2 452251.8 381974.2 23069007 20907.77 847700.2 638290.3
[6,] 746542.3 387398.0 469819.8 397898.4 23528597 22102.37 847700.2 638290.3
        YAF10    YAF11     YAF12   YAF13    YAF14    YAF15    YAF16    YAF17
[1,] 862123.4 55.61797  9062.936 1891552 50919.17 863495.4 1041.897 8.758337
[2,] 862123.4 57.30610  9694.528 2071283 51415.28 852236.8 1041.897 8.933332
[3,] 862123.4 58.99423 10326.120 2251013 51911.39 840978.2 1041.897 9.108327
[4,] 862123.4 60.68236 10957.713 2430744 52407.51 829719.7 1041.897 9.283322
[5,] 862123.4 62.37049 11589.305 2610474 52903.62 818461.1 1041.897 9.458317
[6,] 862123.4 64.05862 12220.897 2790205 53399.73 807202.5 1041.897 9.633312
        YAM1     YAM2     YAM3     YAM4     YAM5     YAM6     YAM7     YAM8
[1,] 71904.8 622496.4 7288.029 18139.21 26.90008 2.751001 1768.626 94.19305
[2,] 71904.8 643385.2 7473.800 18139.21 26.90008 2.763292 1616.066 94.19305
[3,] 71904.8 664274.1 7655.277 18139.21 26.90008 2.775582 1463.505 94.19305
[4,] 71904.8 685163.0 7832.559 18139.21 26.90008 2.787872 1310.945 94.19305
[5,] 71904.8 706051.8 8005.744 18139.21 26.90008 2.800163 1158.384 94.19305
[6,] 71904.8 726940.7 8174.927 18139.21 26.90008 2.812453 1005.824 94.19305
        YAM10    YAM11    YAM12    YAM13    YAM14  YAM15    YAM16    YAM17
[1,] 51.40864 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698
[2,] 45.01771 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698
[3,] 38.62677 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698
[4,] 32.23584 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698
[5,] 25.84490 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698
[6,] 19.45397 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698
        YAM18    YAM19    YAM20   YAM21    YAM22    YAM23    YAM24    YAM25
[1,] 5772.765 98.45844 9383.001 192.915 102.7997 12572.73  9445.22 11882.67
[2,] 5963.491 98.45844 9383.001 192.915 102.7997 13092.52  9840.36 12139.31
[3,] 6154.217 98.45844 9383.001 192.915 102.7997 13612.32 10235.50 12395.95
[4,] 6344.944 98.45844 9383.001 192.915 102.7997 14132.12 10630.64 12652.59
[5,] 6535.670 98.45844 9383.001 192.915 102.7997 14651.91 11025.78 12909.23
[6,] 6726.397 98.45844 9383.001 192.915 102.7997 15171.71 11420.92 13165.87
        YAM26    YAM27    YAM28    YAM29    YAM30     YAB1    YAB2     YAB3
[1,] 25408.03 598.1309 1294.571 8034.943 67724.98 29808.78 7413.43 632495.6
[2,] 25408.03 648.6591 1399.941 8034.943 68437.20 29808.78 7413.43 689561.2
[3,] 25408.03 699.1873 1505.311 8034.943 69149.43 29808.78 7413.43 746626.8
[4,] 25408.03 749.7155 1610.681 8034.943 69861.65 29808.78 7413.43 803692.4
[5,] 25408.03 800.2437 1716.051 8034.943 70573.87 29808.78 7413.43 860758.0
[6,] 25408.03 850.7720 1821.420 8034.943 71286.09 29808.78 7413.43 917823.6
         YAB4     YAB5     YAB6     YAB7     YAB8     YAB9   YAB10    YAB11
[1,] 77761.55 10640.79 765.3444 717627.4 170008.5 249081.6 39097.8 142154.7
[2,] 77761.55 11009.85 787.3006 743153.2 170008.5 268377.3 39097.8 142154.7
[3,] 77761.55 11378.91 809.2567 768679.0 170008.5 287673.0 39097.8 142154.7
[4,] 77761.55 11747.97 831.2129 794204.8 170008.5 306968.7 39097.8 142154.7
[5,] 77761.55 12117.03 853.1691 819730.6 170008.5 326264.5 39097.8 142154.7
[6,] 77761.55 12486.09 875.1253 845256.4 170008.5 345560.2 39097.8 142154.7
        YAB12     YAI1     YAI2     YAI3     YAI4     YAI5    YAI6     YAI7
[1,] 26693.34 1230.370 39176.12 223.3444 2935.279 756.0147 1944587 21800234
[2,] 26827.99 1274.384 39176.12 223.3444 2935.279 756.0147 2035542 21800234
[3,] 26962.64 1318.399 39176.12 223.3444 2935.279 756.0147 2126498 21800234
[4,] 27097.28 1362.414 39176.12 223.3444 2935.279 756.0147 2217453 21800234
[5,] 27231.93 1406.428 39176.12 223.3444 2935.279 756.0147 2308408 21800234
[6,] 27366.58 1450.443 39176.12 223.3444 2935.279 756.0147 2399363 21800234
         YAI8     YAI9    YAI10    YAI11    YAI12    YAI13    YAI14    YAI15
[1,] 8585.218 279.6960 219148.7 627.7966 1575.805 1294.276 810.0796 246.3978
[2,] 8585.218 299.0945 226157.3 627.7966 1679.404 1550.172 810.0796 259.6593
[3,] 8585.218 318.4930 233165.9 627.7966 1783.002 1806.068 810.0796 272.9209
[4,] 8585.218 337.8915 240174.5 627.7966 1886.601 2061.965 810.0796 286.1824
[5,] 8585.218 357.2900 247183.1 627.7966 1990.200 2317.861 810.0796 299.4439
[6,] 8585.218 376.6884 254191.8 627.7966 2093.798 2573.757 810.0796 312.7054
        YAI16    YAI17    YAI18    YAI19    YAI20    YAI21    YAI22    YAI23
[1,] 150.4702 1272.175 114.9165 38.20008 14.05925 1294.571 3116.417 23.35369
[2,] 161.7391 1272.175 114.9165 38.20008 14.05925 1399.941 3116.417 23.35369
[3,] 173.0080 1272.175 114.9165 38.20008 14.05925 1505.311 3116.417 23.35369
[4,] 184.2770 1272.175 114.9165 38.20008 14.05925 1610.681 3116.417 23.35369
[5,] 195.5459 1272.175 114.9165 38.20008 14.05925 1716.051 3116.417 23.35369
[6,] 206.8149 1272.175 114.9165 38.20008 14.05925 1821.420 3116.417 23.35369
        YAI24    YAI25    YAI26    YAI27    YAI28    YAI29    YAI30    YAI31
[1,] 144346.9 60.66101 682.1895 4366.951 387.0890 151.2821 16.75260 6.380076
[2,] 153609.4 64.52041 697.7193 4809.599 402.4771 157.9637 17.76071 6.380076
[3,] 162872.0 68.37980 713.2492 5252.247 417.8652 164.6454 18.76882 6.380076
[4,] 172134.5 72.23920 728.7790 5694.895 433.2533 171.3271 19.77693 6.380076
[5,] 181397.1 76.09860 744.3089 6137.543 448.6414 178.0087 20.78504 6.380076
[6,] 190659.6 79.95799 759.8388 6580.191 464.0295 184.6904 21.79315 6.380076
     YAI32    YAI33    YAI34    YAI35     YAG1     YAG2      YAG3     YAG4
[1,]  14.2 7.863819 3.334205 2.799162 236.2488 52.51979  92.29229 10.83798
[2,]  14.2 7.863819 3.334205 2.799162 243.8410 52.51979  99.96504 10.83798
[3,]  14.2 7.863819 3.334205 2.799162 251.4332 52.51979 107.63780 10.83798
[4,]  14.2 7.863819 3.334205 2.799162 259.0254 52.51979 115.31055 10.83798
[5,]  14.2 7.863819 3.334205 2.799162 266.6176 52.51979 122.98330 10.83798
[6,]  14.2 7.863819 3.334205 2.799162 274.2099 52.51979 130.65605 10.83798
         YAG5     YAG6     YAG7     YAG8     YAG9    YAG10    YAG11    YAG12
[1,] 119.9995 105.3229 112.8678 187.9984 125.9992 92.39959 366156.5 107237.2
[2,] 124.9992 105.3229 112.8678 187.9984 125.9992 92.39959 379417.3 107237.2
[3,] 129.9988 105.3229 112.8678 187.9984 125.9992 92.39959 392678.1 107237.2
[4,] 134.9985 105.3229 112.8678 187.9984 125.9992 92.39959 405938.8 107237.2
[5,] 139.9981 105.3229 112.8678 187.9984 125.9992 92.39959 419199.6 107237.2
[6,] 144.9978 105.3229 112.8678 187.9984 125.9992 92.39959 432460.4 107237.2
         YAG13    YAG14    YAG15    YAG16    YAG17    YAG18    YAG19    YAG20
[1,]  96645.48 4317.518 30435.68 471558.6 41.41975 597.9932 616.1694 877.4688
[2,] 100051.24 4317.518 31600.27 488490.1 41.41975 597.9932 663.3367 896.8383
[3,] 103457.00 4317.518 32764.86 505421.5 41.41975 597.9932 710.5040 916.2079
[4,] 106862.75 4317.518 33929.45 522353.0 41.41975 597.9932 757.6713 935.5774
[5,] 110268.51 4317.518 35094.03 539284.5 41.41975 597.9932 804.8386 954.9469
[6,] 113674.27 4317.518 36258.62 556215.9 41.41975 597.9932 852.0059 974.3164
        YAG21    YAG22    YAG23    YAG24    YAG25    YAG26    YAG27    YAG28
[1,] 5.676057 10.28459 137.1325 65.55742 22.06471 11.73084 6.194973 7.658353
[2,] 5.861596 10.66136 142.7652 67.58464 22.76828 12.24912 6.545724 7.920919
[3,] 6.047134 11.03812 148.3979 69.61186 23.47184 12.76740 6.896474 8.183485
[4,] 6.232673 11.41489 154.0306 71.63908 24.17541 13.28567 7.247224 8.446052
[5,] 6.418211 11.79165 159.6634 73.66630 24.87898 13.80395 7.597974 8.708618
[6,] 6.603750 12.16842 165.2961 75.69353 25.58254 14.32223 7.948724 8.971185
        YAG29    YAG30     YAC1     YAC2     YAC3     YAC4      YAC5     YAC6
[1,] 8.055765 4.436833 75.11300 27.10459 18.73374 23.77300  95.77583 19.50443
[2,] 8.411540 4.673677 77.04760 27.98003 19.72020 26.30834  98.62324 19.50443
[3,] 8.767315 4.910521 78.98220 28.85547 20.70665 28.84368 101.47066 19.50443
[4,] 9.123091 5.147365 80.91680 29.73091 21.69311 31.37902 104.31808 19.50443
[5,] 9.478866 5.384209 82.85141 30.60635 22.67957 33.91435 107.16550 19.50443
[6,] 9.834641 5.621053 84.78601 31.48179 23.66602 36.44969 110.01291 19.50443
         YAC7     YAC8     YAC9    YAC10    YAC11    YAC12    YAC13    YAC14
[1,] 32.33359 28.28980 42.73003 73781.77 32065.89 53562.68 39957.31 52763.99
[2,] 33.03120 30.90142 46.52828 73781.77 32844.40 56028.30 41191.43 52763.99
[3,] 33.72881 33.51303 50.32652 73781.77 33622.91 58493.91 42425.55 52763.99
[4,] 34.42642 36.12465 54.12477 73781.77 34401.42 60959.53 43659.67 52763.99
[5,] 35.12403 38.73626 57.92302 73781.77 35179.92 63425.14 44893.79 52763.99
[6,] 35.82165 41.34788 61.72126 73781.77 35958.43 65890.76 46127.90 52763.99
        YAC15    YAC16    YAC17    YAC18    YAC19    YAC20    YAC21    YAC22
[1,] 58574.27 25962.29 32594.29 54.59722 31385663 5325.901 2082.296 2091.260
[2,] 62860.50 25962.29 33675.17 56.69452 31385663 5539.986 2152.363 2239.474
[3,] 67146.73 25962.29 34756.04 58.79181 31385663 5754.071 2222.431 2387.689
[4,] 71432.96 25962.29 35836.92 60.88911 31385663 5968.156 2292.499 2535.903
[5,] 75719.19 25962.29 36917.80 62.98641 31385663 6182.241 2362.566 2684.118
[6,] 80005.42 25962.29 37998.67 65.08370 31385663 6396.326 2432.634 2832.332
        YAC23    YAC24    YAC25    YAC26    YAC27    YAC28    YAC29     YAD1
[1,] 1797.065 1803.988 3382.958 890.9938 1686.843 2395.335 2045.002 114.6321
[2,] 1892.605 1803.988 3600.915 890.9938 1824.681 2499.652 2045.002 114.6321
[3,] 1988.145 1803.988 3818.872 890.9938 1962.520 2603.968 2045.002 114.6321
[4,] 2083.684 1803.988 4036.828 890.9938 2100.358 2708.285 2045.002 114.6321
[5,] 2179.224 1803.988 4254.785 890.9938 2238.196 2812.602 2045.002 114.6321
[6,] 2274.764 1803.988 4472.742 890.9938 2376.035 2916.918 2045.002 114.6321
         YAD2     YAD3     YAD4     YAD5     YAD6     YAD7     YAD8     YAD9
[1,] 36599.87 290.6517 1917.219 491.9706 448.7009 438.1286 886.3374 888.2836
[2,] 36697.57 291.1678 1917.219 491.9706 448.7009 439.4655 889.4333 888.2836
[3,] 36793.12 291.6615 1917.219 491.9706 448.7009 440.8024 892.5292 888.2836
[4,] 36886.59 292.1336 1917.219 491.9706 448.7009 442.1393 895.6251 888.2836
[5,] 36978.01 292.5853 1917.219 491.9706 448.7009 443.4762 898.7209 888.2836
[6,] 37067.42 293.0172 1917.219 491.9706 448.7009 444.8132 901.8168 888.2836
        YAD10    YAD11   YAD12   YAD13    YAD14    YAD15    YAD16    YAD17
[1,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6
[2,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6
[3,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6
[4,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6
[5,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6
[6,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6
        YAD18   YAD19    YAD20    YAD21    YAD22    YAD23    YAD24    YAD25
[1,] 2.334264 1551118 638.9945 26631.33 469.7187 442.9032 326656.7 28178.30
[2,] 2.334264 1551118 638.9945 26820.24 469.7187 442.9032 326656.7 28362.21
[3,] 2.334264 1551118 638.9945 27009.14 469.7187 442.9032 326656.7 28546.12
[4,] 2.334264 1551118 638.9945 27198.05 469.7187 442.9032 326656.7 28730.02
[5,] 2.334264 1551118 638.9945 27386.95 469.7187 442.9032 326656.7 28913.93
[6,] 2.334264 1551118 638.9945 27575.86 469.7187 442.9032 326656.7 29097.83
        YAD26    YAD27    YAD28    YAD29    YAD30
[1,] 313613.9 10254.09 7821.031 56.20631 1016.286
[2,] 313613.9 10254.09 7821.031 56.20631 1016.286
[3,] 313613.9 10254.09 7821.031 56.20631 1016.286
[4,] 313613.9 10254.09 7821.031 56.20631 1016.286
[5,] 313613.9 10254.09 7821.031 56.20631 1016.286
[6,] 313613.9 10254.09 7821.031 56.20631 1016.286

$forecasts$rw
       YAF2   YAF3   YAF4   YAF5     YAF6    YAF7   YAF8   YAF9  YAF10 YAF11
[1,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93
[2,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93
[3,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93
[4,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93
[5,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93
[6,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93
     YAF12   YAF13 YAF14  YAF15  YAF16   YAF17  YAM1   YAM2    YAM3  YAM4 YAM5
[1,]  8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9
[2,]  8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9
[3,]  8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9
[4,]  8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9
[5,]  8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9
[6,]  8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9
        YAM6   YAM7 YAM8 YAM10    YAM11    YAM12 YAM13 YAM14 YAM15 YAM16 YAM17
[1,] 2.74031 1919.4 71.6  57.8 20525000 13056000  3482   811   770 100.8   175
[2,] 2.74031 1919.4 71.6  57.8 20525000 13056000  3482   811   770 100.8   175
[3,] 2.74031 1919.4 71.6  57.8 20525000 13056000  3482   811   770 100.8   175
[4,] 2.74031 1919.4 71.6  57.8 20525000 13056000  3482   811   770 100.8   175
[5,] 2.74031 1919.4 71.6  57.8 20525000 13056000  3482   811   770 100.8   175
[6,] 2.74031 1919.4 71.6  57.8 20525000 13056000  3482   811   770 100.8   175
     YAM18 YAM19 YAM20  YAM21 YAM22 YAM23 YAM24 YAM25 YAM26 YAM27 YAM28 YAM29
[1,]  5582 101.4  9383 207.95 102.8 12053  9050 11626 25408   559  1219  8035
[2,]  5582 101.4  9383 207.95 102.8 12053  9050 11626 25408   559  1219  8035
[3,]  5582 101.4  9383 207.95 102.8 12053  9050 11626 25408   559  1219  8035
[4,]  5582 101.4  9383 207.95 102.8 12053  9050 11626 25408   559  1219  8035
[5,]  5582 101.4  9383 207.95 102.8 12053  9050 11626 25408   559  1219  8035
[6,]  5582 101.4  9383 207.95 102.8 12053  9050 11626 25408   559  1219  8035
     YAM30  YAB1 YAB2   YAB3  YAB4  YAB5 YAB6   YAB7   YAB8   YAB9 YAB10  YAB11
[1,] 74667 29809 7555 588478 80389 10185  660 692102 147233 229789 39098 142157
[2,] 74667 29809 7555 588478 80389 10185  660 692102 147233 229789 39098 142157
[3,] 74667 29809 7555 588478 80389 10185  660 692102 147233 229789 39098 142157
[4,] 74667 29809 7555 588478 80389 10185  660 692102 147233 229789 39098 142157
[5,] 74667 29809 7555 588478 80389 10185  660 692102 147233 229789 39098 142157
[6,] 74667 29809 7555 588478 80389 10185  660 692102 147233 229789 39098 142157
     YAB12 YAI1  YAI2 YAI3 YAI4 YAI5    YAI6     YAI7   YAI8 YAI9  YAI10 YAI11
[1,] 26869 1191 39177  365 2977  756 1859860 21800200 8800.8  270 212140 632.6
[2,] 26869 1191 39177  365 2977  756 1859860 21800200 8800.8  270 212140 632.6
[3,] 26869 1191 39177  365 2977  756 1859860 21800200 8800.8  270 212140 632.6
[4,] 26869 1191 39177  365 2977  756 1859860 21800200 8800.8  270 212140 632.6
[5,] 26869 1191 39177  365 2977  756 1859860 21800200 8800.8  270 212140 632.6
[6,] 26869 1191 39177  365 2977  756 1859860 21800200 8800.8  270 212140 632.6
      YAI12  YAI13 YAI14 YAI15 YAI16  YAI17 YAI18 YAI19  YAI20 YAI21  YAI22
[1,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5  38.2 13.936  1219 3116.4
[2,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5  38.2 13.936  1219 3116.4
[3,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5  38.2 13.936  1219 3116.4
[4,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5  38.2 13.936  1219 3116.4
[5,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5  38.2 13.936  1219 3116.4
[6,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5  38.2 13.936  1219 3116.4
     YAI23  YAI24 YAI25 YAI26 YAI27 YAI28 YAI29 YAI30 YAI31 YAI32 YAI33 YAI34
[1,]    24 131194  56.8   470  3840 371.7 144.6 16.34  6.38  14.2  9.33  3.34
[2,]    24 131194  56.8   470  3840 371.7 144.6 16.34  6.38  14.2  9.33  3.34
[3,]    24 131194  56.8   470  3840 371.7 144.6 16.34  6.38  14.2  9.33  3.34
[4,]    24 131194  56.8   470  3840 371.7 144.6 16.34  6.38  14.2  9.33  3.34
[5,]    24 131194  56.8   470  3840 371.7 144.6 16.34  6.38  14.2  9.33  3.34
[6,]    24 131194  56.8   470  3840 371.7 144.6 16.34  6.38  14.2  9.33  3.34
     YAI35  YAG1  YAG2  YAG3  YAG4 YAG5   YAG6 YAG7 YAG8 YAG9 YAG10  YAG11
[1,]  2.84 237.6 52.52 84.66 11.39  115 107.69  117  188  126  92.4 356556
[2,]  2.84 237.6 52.52 84.66 11.39  115 107.69  117  188  126  92.4 356556
[3,]  2.84 237.6 52.52 84.66 11.39  115 107.69  117  188  126  92.4 356556
[4,]  2.84 237.6 52.52 84.66 11.39  115 107.69  117  188  126  92.4 356556
[5,]  2.84 237.6 52.52 84.66 11.39  115 107.69  117  188  126  92.4 356556
[6,]  2.84 237.6 52.52 84.66 11.39  115 107.69  117  188  126  92.4 356556
      YAG12 YAG13 YAG14 YAG15  YAG16 YAG17 YAG18 YAG19 YAG20 YAG21 YAG22 YAG23
[1,] 107238 93951  6347 30278 460613 41.42   598   569 858.1   5.6  10.1 131.5
[2,] 107238 93951  6347 30278 460613 41.42   598   569 858.1   5.6  10.1 131.5
[3,] 107238 93951  6347 30278 460613 41.42   598   569 858.1   5.6  10.1 131.5
[4,] 107238 93951  6347 30278 460613 41.42   598   569 858.1   5.6  10.1 131.5
[5,] 107238 93951  6347 30278 460613 41.42   598   569 858.1   5.6  10.1 131.5
[6,] 107238 93951  6347 30278 460613 41.42   598   569 858.1   5.6  10.1 131.5
     YAG24 YAG25 YAG26 YAG27 YAG28 YAG29 YAG30  YAC1  YAC2 YAC3  YAC4  YAC5
[1,]  63.1  22.1  11.3     6   7.4   7.7   4.2 74.51 27.65 17.7 22.09 95.65
[2,]  63.1  22.1  11.3     6   7.4   7.7   4.2 74.51 27.65 17.7 22.09 95.65
[3,]  63.1  22.1  11.3     6   7.4   7.7   4.2 74.51 27.65 17.7 22.09 95.65
[4,]  63.1  22.1  11.3     6   7.4   7.7   4.2 74.51 27.65 17.7 22.09 95.65
[5,]  63.1  22.1  11.3     6   7.4   7.7   4.2 74.51 27.65 17.7 22.09 95.65
[6,]  63.1  22.1  11.3     6   7.4   7.7   4.2 74.51 27.65 17.7 22.09 95.65
      YAC6  YAC7  YAC8  YAC9 YAC10 YAC11 YAC12 YAC13 YAC14 YAC15 YAC16 YAC17
[1,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460
[2,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460
[3,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460
[4,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460
[5,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460
[6,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460
     YAC18    YAC19 YAC20 YAC21 YAC22 YAC23 YAC24 YAC25 YAC26 YAC27 YAC28 YAC29
[1,]  52.5 31441200  5141  2017  1955  1654  1804  3165   891  1549  2291  2045
[2,]  52.5 31441200  5141  2017  1955  1654  1804  3165   891  1549  2291  2045
[3,]  52.5 31441200  5141  2017  1955  1654  1804  3165   891  1549  2291  2045
[4,]  52.5 31441200  5141  2017  1955  1654  1804  3165   891  1549  2291  2045
[5,]  52.5 31441200  5141  2017  1955  1654  1804  3165   891  1549  2291  2045
[6,]  52.5 31441200  5141  2017  1955  1654  1804  3165   891  1549  2291  2045
     YAD1  YAD2 YAD3 YAD4 YAD5 YAD6 YAD7 YAD8 YAD9 YAD10 YAD11 YAD12 YAD13
[1,]  142 36500  298 1546  522  492  487  979  937  1018  4088  37.1  39.8
[2,]  142 36500  298 1546  522  492  487  979  937  1018  4088  37.1  39.8
[3,]  142 36500  298 1546  522  492  487  979  937  1018  4088  37.1  39.8
[4,]  142 36500  298 1546  522  492  487  979  937  1018  4088  37.1  39.8
[5,]  142 36500  298 1546  522  492  487  979  937  1018  4088  37.1  39.8
[6,]  142 36500  298 1546  522  492  487  979  937  1018  4088  37.1  39.8
     YAD14 YAD15 YAD16  YAD17 YAD18   YAD19 YAD20 YAD21 YAD22 YAD23  YAD24
[1,]   963  23.2   9.3 413000  2.35 1577360   639 26441   473   446 333594
[2,]   963  23.2   9.3 413000  2.35 1577360   639 26441   473   446 333594
[3,]   963  23.2   9.3 413000  2.35 1577360   639 26441   473   446 333594
[4,]   963  23.2   9.3 413000  2.35 1577360   639 26441   473   446 333594
[5,]   963  23.2   9.3 413000  2.35 1577360   639 26441   473   446 333594
[6,]   963  23.2   9.3 413000  2.35 1577360   639 26441   473   446 333594
     YAD25  YAD26 YAD27 YAD28 YAD29 YAD30
[1,] 27995 322404 10254  7821 56.49  1016
[2,] 27995 322404 10254  7821 56.49  1016
[3,] 27995 322404 10254  7821 56.49  1016
[4,] 27995 322404 10254  7821 56.49  1016
[5,] 27995 322404 10254  7821 56.49  1016
[6,] 27995 322404 10254  7821 56.49  1016

$forecasts$rwd
         YAF2     YAF3     YAF4     YAF5     YAF6     YAF7      YAF8     YAF9
[1,] 579581.0 400921.2 378573.6 365733.4 19234508 15566.79  904964.3 673803.7
[2,] 605761.9 417802.4 394940.2 381383.8 19716615 16153.68  962222.7 709311.4
[3,] 631942.9 434683.5 411306.8 397034.2 20198723 16740.58 1019481.0 744819.1
[4,] 658123.8 451564.7 427673.4 412684.6 20680830 17327.47 1076739.3 780326.8
[5,] 684304.8 468445.9 444040.0 428335.0 21162938 17914.36 1133997.7 815834.5
[6,] 710485.7 485327.1 460406.5 443985.5 21645045 18501.25 1191256.0 851342.2
         YAF10 YAF11   YAF12   YAF13    YAF14     YAF15    YAF16    YAF17
[1,]  906621.4 55.13  8765.6 1775160 51406.53  908663.9 1084.355 8.764490
[2,]  951113.8 56.33  9084.2 1838480 52390.06  950829.8 1126.809 8.945009
[3,]  995606.1 57.53  9402.8 1901800 53373.59  992995.7 1169.264 9.125529
[4,] 1040098.5 58.73  9721.4 1965120 54357.12 1035161.6 1211.718 9.306048
[5,] 1084590.9 59.93 10040.0 2028441 55340.65 1077327.5 1254.173 9.486568
[6,] 1129083.2 61.13 10358.6 2091761 56324.18 1119493.4 1296.627 9.667087
         YAM1     YAM2     YAM3     YAM4     YAM5     YAM6     YAM7      YAM8
[1,] 74969.09 697948.7 7089.829 18996.05 24.85833 2.753552 2031.144  76.60833
[2,] 78183.18 729673.4 7323.188 19853.10 22.81667 2.766793 2142.888  81.61667
[3,] 81397.27 761398.1 7556.547 20710.14 20.77500 2.780035 2254.631  86.62500
[4,] 84611.36 793122.9 7789.906 21567.19 18.73333 2.793276 2366.375  91.63333
[5,] 87825.45 824847.6 8023.265 22424.24 16.69167 2.806518 2478.119  96.64167
[6,] 91039.55 856572.3 8256.624 23281.29 14.65000 2.819759 2589.863 101.65000
        YAM10    YAM11    YAM12    YAM13    YAM14    YAM15    YAM16    YAM17
[1,] 60.54762 20667008 13014517 3527.625 822.6842 780.3333 101.9238 179.9231
[2,] 63.29524 20809017 12973033 3573.250 834.3684 790.6667 103.0476 184.8462
[3,] 66.04286 20951025 12931550 3618.875 846.0526 801.0000 104.1714 189.7692
[4,] 68.79048 21093033 12890067 3664.500 857.7368 811.3333 105.2952 194.6923
[5,] 71.53810 21235042 12848583 3710.125 869.4211 821.6667 106.4190 199.6154
[6,] 74.28571 21377050 12807100 3755.750 881.1053 832.0000 107.5429 204.5385
        YAM18    YAM19   YAM20    YAM21    YAM22    YAM23    YAM24   YAM25
[1,] 5773.286 102.6857 9394.15 209.1556 105.1143 12469.10  9352.15 11898.3
[2,] 5964.571 103.9714 9405.30 210.3611 107.4286 12885.19  9654.30 12170.6
[3,] 6155.857 105.2571 9416.45 211.5667 109.7429 13301.29  9956.45 12442.9
[4,] 6347.143 106.5429 9427.60 212.7722 112.0571 13717.38 10258.60 12715.2
[5,] 6538.429 107.8286 9438.75 213.9778 114.3714 14133.48 10560.75 12987.5
[6,] 6729.714 109.1143 9449.90 215.1833 116.6857 14549.57 10862.90 13259.8
       YAM26  YAM27   YAM28    YAM29    YAM30     YAB1     YAB2     YAB3
[1,] 25885.5 584.95 1267.55 8074.688 76266.65 31148.35 7913.095 621170.9
[2,] 26363.0 610.90 1316.10 8114.375 77866.30 32487.70 8271.190 653863.9
[3,] 26840.5 636.85 1364.65 8154.062 79465.96 33827.05 8629.286 686556.8
[4,] 27318.0 662.80 1413.20 8193.750 81065.61 35166.40 8987.381 719249.8
[5,] 27795.5 688.75 1461.75 8233.438 82665.26 36505.75 9345.476 751942.7
[6,] 28273.0 714.70 1510.30 8273.125 84264.91 37845.10 9703.571 784635.7
          YAB4     YAB5     YAB6     YAB7     YAB8     YAB9    YAB10    YAB11
[1,]  84186.67 10547.31 672.5814 718453.1 148108.9 250283.4 41750.27 147471.1
[2,]  87984.33 10909.62 685.1628 744804.2 148984.8 270777.7 44402.55 152785.2
[3,]  91782.00 11271.94 697.7442 771155.3 149860.7 291272.1 47054.82 158099.3
[4,]  95579.67 11634.25 710.3256 797506.4 150736.6 311766.5 49707.09 163413.4
[5,]  99377.33 11996.56 722.9070 823857.5 151612.5 332260.8 52359.36 168727.5
[6,] 103175.00 12358.88 735.4884 850208.5 152488.5 352755.2 55011.64 174041.5
        YAB12     YAI1     YAI2     YAI3     YAI4     YAI5    YAI6     YAI7
[1,] 27054.21 1257.088 40285.68 371.7368 3014.289 759.9211 1910418 22286105
[2,] 27239.42 1323.176 41394.36 378.4737 3051.579 763.8421 1960976 22772011
[3,] 27424.63 1389.265 42503.04 385.2105 3088.868 767.7632 2011534 23257916
[4,] 27609.84 1455.353 43611.72 391.9474 3126.158 771.6842 2062092 23743822
[5,] 27795.05 1521.441 44720.40 398.6842 3163.447 775.6053 2112651 24229727
[6,] 27980.26 1587.529 45829.08 405.4211 3200.737 779.5263 2163209 24715632
          YAI8  YAI9  YAI10    YAI11    YAI12    YAI13     YAI14    YAI15
[1,]  9174.941 290.2 217400 662.7529 1558.371 1098.188  870.4231 260.4941
[2,]  9549.082 310.4 222660 692.9059 1644.541 1157.976  930.7462 273.8882
[3,]  9923.224 330.6 227920 723.0588 1730.712 1217.765  991.0692 287.2824
[4,] 10297.365 350.8 233180 753.2118 1816.882 1277.553 1051.3923 300.6765
[5,] 10671.506 371.0 238440 783.3647 1903.053 1337.341 1111.7154 314.0706
[6,] 11045.647 391.2 243700 813.5176 1989.224 1397.129 1172.0385 327.4647
        YAI16    YAI17     YAI18    YAI19    YAI20   YAI21    YAI22    YAI23
[1,] 146.8882 1332.518 108.93833 39.08333 13.74358 1267.55 3205.167 24.22632
[2,] 154.5765 1392.835 106.37667 39.96667 13.55117 1316.10 3293.935 24.45263
[3,] 162.2647 1453.153 103.81500 40.85000 13.35875 1364.65 3382.702 24.67895
[4,] 169.9529 1513.471 101.25333 41.73333 13.16633 1413.20 3471.470 24.90526
[5,] 177.6412 1573.788  98.69167 42.61667 12.97392 1461.75 3560.237 25.13158
[6,] 185.3294 1634.106  96.13000 43.50000 12.78150 1510.30 3649.005 25.35789
      YAI24    YAI25    YAI26    YAI27    YAI28    YAI29  YAI30    YAI31
[1,] 135512 59.07368 472.9444 4044.167 388.0684 150.4105 17.555 6.552727
[2,] 139830 61.34737 475.8889 4248.333 404.4368 156.2211 18.770 6.725455
[3,] 144148 63.62105 478.8333 4452.500 420.8053 162.0316 19.985 6.898182
[4,] 148466 65.89474 481.7778 4656.667 437.1737 167.8421 21.200 7.070909
[5,] 152784 68.16842 484.7222 4860.833 453.5421 173.6526 22.415 7.243636
[6,] 157102 70.44211 487.6667 5065.000 469.9105 179.4632 23.630 7.416364
        YAI32     YAI33 YAI34    YAI35     YAG1     YAG2    YAG3     YAG4
[1,] 14.43333  9.511667  3.46 2.850909 245.9575 53.90333  88.745 11.84167
[2,] 14.66667  9.693333  3.58 2.861818 254.3150 55.28667  92.830 12.29333
[3,] 14.90000  9.875000  3.70 2.872727 262.6725 56.67000  96.915 12.74500
[4,] 15.13333 10.056667  3.82 2.883636 271.0300 58.05333 101.000 13.19667
[5,] 15.36667 10.238333  3.94 2.894545 279.3875 59.43667 105.085 13.64833
[6,] 15.60000 10.420000  4.06 2.905455 287.7450 60.82000 109.170 14.10000
         YAG5     YAG6     YAG7     YAG8     YAG9     YAG10    YAG11    YAG12
[1,] 118.8125 113.3922 117.5833 191.3611 127.2121  95.52632 370305.5 113285.7
[2,] 122.6250 119.0944 118.1667 194.7222 128.4242  98.65263 384055.0 119333.3
[3,] 126.4375 124.7967 118.7500 198.0833 129.6364 101.77895 397804.5 125381.0
[4,] 130.2500 130.4989 119.3333 201.4444 130.8485 104.90526 411554.0 131428.7
[5,] 134.0625 136.2011 119.9167 204.8056 132.0606 108.03158 425303.5 137476.3
[6,] 137.8750 141.9033 120.5000 208.1667 133.2727 111.15789 439053.0 143524.0
        YAG13  YAG14    YAG15    YAG16    YAG17    YAG18    YAG19    YAG20
[1,]  97293.5 6330.5 31650.58 478816.8 42.49533 630.8182 599.6364 868.4811
[2,] 100636.0 6314.0 33023.17 497020.7 43.57067 663.6364 630.2727 878.8622
[3,] 103978.5 6297.5 34395.75 515224.5 44.64600 696.4545 660.9091 889.2432
[4,] 107321.0 6281.0 35768.33 533428.3 45.72133 729.2727 691.5455 899.6243
[5,] 110663.5 6264.5 37140.92 551632.2 46.79667 762.0909 722.1818 910.0054
[6,] 114006.0 6248.0 38513.50 569836.0 47.87200 794.9091 752.8182 920.3865
        YAG21    YAG22    YAG23    YAG24    YAG25    YAG26 YAG27    YAG28
[1,] 5.807143 10.48571 137.5071 65.54286 22.85714 11.62857  6.25 7.664286
[2,] 6.014286 10.87143 143.5143 67.98571 23.61429 11.95714  6.50 7.928571
[3,] 6.221429 11.25714 149.5214 70.42857 24.37143 12.28571  6.75 8.192857
[4,] 6.428571 11.64286 155.5286 72.87143 25.12857 12.61429  7.00 8.457143
[5,] 6.635714 12.02857 161.5357 75.31429 25.88571 12.94286  7.25 8.721429
[6,] 6.842857 12.41429 167.5429 77.75714 26.64286 13.27143  7.50 8.985714
        YAG29    YAG30    YAC1    YAC2  YAC3     YAC4      YAC5     YAC6   YAC7
[1,] 7.935714 4.342857 76.5825 28.6575 18.36 23.45917  98.85917 20.28667 33.625
[2,] 8.171429 4.485714 78.6550 29.6650 19.02 24.82833 102.06833 20.73333 34.560
[3,] 8.407143 4.628571 80.7275 30.6725 19.68 26.19750 105.27750 21.18000 35.495
[4,] 8.642857 4.771429 82.8000 31.6800 20.34 27.56667 108.48667 21.62667 36.430
[5,] 8.878571 4.914286 84.8725 32.6875 21.00 28.93583 111.69583 22.07333 37.365
[6,] 9.114286 5.057143 86.9450 33.6950 21.66 30.30500 114.90500 22.52000 38.300
        YAC8     YAC9    YAC10    YAC11    YAC12    YAC13    YAC14    YAC15
[1,] 26.5675 40.89083 75474.42 32767.92 54381.67 41238.08 56175.58 57110.08
[2,] 27.5050 42.85167 77166.83 33675.83 56928.33 42442.17 59401.17 59932.17
[3,] 28.4425 44.81250 78859.25 34583.75 59475.00 43646.25 62626.75 62754.25
[4,] 29.3800 46.77333 80551.67 35491.67 62021.67 44850.33 65852.33 65576.33
[5,] 30.3175 48.73417 82244.08 36399.58 64568.33 46054.42 69077.92 68398.42
[6,] 31.2550 50.69500 83936.50 37307.50 67115.00 47258.50 72303.50 71220.50
        YAC16   YAC17    YAC18    YAC19    YAC20    YAC21    YAC22 YAC23  YAC24
[1,] 27463.75 33610.5 54.46667 32175926 5350.167 2083.917 2047.833  1743 1886.5
[2,] 28052.50 34761.0 56.43333 32910651 5559.333 2150.833 2140.667  1832 1969.0
[3,] 28641.25 35911.5 58.40000 33645377 5768.500 2217.750 2233.500  1921 2051.5
[4,] 29230.00 37062.0 60.36667 34380102 5977.667 2284.667 2326.333  2010 2134.0
[5,] 29818.75 38212.5 62.33333 35114828 6186.833 2351.583 2419.167  2099 2216.5
[6,] 30407.50 39363.0 64.30000 35849554 6396.000 2418.500 2512.000  2188 2299.0
        YAC25     YAC26 YAC27    YAC28    YAC29  YAD1     YAD2     YAD3
[1,] 3319.417  937.6667  1639 2406.917 2086.083 140.3 36659.21 299.9737
[2,] 3473.833  984.3333  1729 2522.833 2127.167 138.6 36818.42 301.9474
[3,] 3628.250 1031.0000  1819 2638.750 2168.250 136.9 36977.63 303.9211
[4,] 3782.667 1077.6667  1909 2754.667 2209.333 135.2 37136.84 305.8947
[5,] 3937.083 1124.3333  1999 2870.583 2250.417 133.5 37296.05 307.8684
[6,] 4091.500 1171.0000  2089 2986.500 2291.500 131.8 37455.26 309.8421
         YAD4     YAD5     YAD6     YAD7      YAD8     YAD9    YAD10    YAD11
[1,] 1480.875 522.6316 495.1579 490.1053  985.2632 938.0526 1019.395 4178.429
[2,] 1415.750 523.2632 498.3158 493.2105  991.5263 939.1053 1020.789 4268.857
[3,] 1350.625 523.8947 501.4737 496.3158  997.7895 940.1579 1022.184 4359.286
[4,] 1285.500 524.5263 504.6316 499.4211 1004.0526 941.2105 1023.579 4449.714
[5,] 1220.375 525.1579 507.7895 502.5263 1010.3158 942.2632 1024.974 4540.143
[6,] 1155.250 525.7895 510.9474 505.6316 1016.5789 943.3158 1026.368 4630.571
        YAD12    YAD13    YAD14   YAD15  YAD16    YAD17    YAD18   YAD19
[1,] 36.82857 39.75714 946.7143 23.0125 9.2625 414118.2 2.339091 1576652
[2,] 36.55714 39.71429 930.4286 22.8250 9.2250 415236.3 2.328182 1575943
[3,] 36.28571 39.67143 914.1429 22.6375 9.1875 416354.5 2.317273 1575235
[4,] 36.01429 39.62857 897.8571 22.4500 9.1500 417472.6 2.306364 1574526
[5,] 35.74286 39.58571 881.5714 22.2625 9.1125 418590.8 2.295455 1573818
[6,] 35.47143 39.54286 865.2857 22.0750 9.0750 419708.9 2.284545 1573109
        YAD20   YAD21    YAD22    YAD23    YAD24    YAD25    YAD26     YAD27
[1,] 666.3333 26604.5 476.2353 449.1176 335793.7 28127.57 325039.1 10123.182
[2,] 693.6667 26768.0 479.4706 452.2353 337993.3 28260.14 327674.2  9992.364
[3,] 721.0000 26931.5 482.7059 455.3529 340193.0 28392.71 330309.2  9861.545
[4,] 748.3333 27095.0 485.9412 458.4706 342392.7 28525.29 332944.3  9730.727
[5,] 775.6667 27258.5 489.1765 461.5882 344592.3 28657.86 335579.4  9599.909
[6,] 803.0000 27422.0 492.4118 464.7059 346792.0 28790.43 338214.5  9469.091
        YAD28    YAD29    YAD30
[1,] 7764.909 56.51762 1037.524
[2,] 7708.818 56.54524 1059.048
[3,] 7652.727 56.57286 1080.571
[4,] 7596.636 56.60048 1102.095
[5,] 7540.545 56.62810 1123.619
[6,] 7484.455 56.65571 1145.143

$forecasts$theta
         YAF2     YAF3     YAF4     YAF5     YAF6     YAF7      YAF8     YAF9
[1,] 565938.8 394342.6 370630.6 343795.6 19501512 15253.27  876501.3 653956.4
[2,] 578486.4 404640.6 379052.1 351953.9 19800960 15535.55  905299.5 669620.9
[3,] 591034.0 414938.7 387473.7 360112.2 20100408 15817.82  934097.6 685285.4
[4,] 603581.5 425236.7 395895.2 368270.5 20399856 16100.09  962895.8 700949.8
[5,] 616129.1 435534.8 404316.7 376428.8 20699304 16382.36  991694.0 716614.3
[6,] 628676.6 445832.8 412738.3 384587.1 20998752 16664.63 1020492.1 732278.8
        YAF10    YAF11    YAF12   YAF13    YAF14     YAF15    YAF16    YAF17
[1,] 883950.0 54.48800 8602.318 1740132 50890.50  892079.5 1066.141 8.675195
[2,] 905774.4 55.04627 8757.663 1768449 51357.94  917899.2 1090.382 8.766434
[3,] 927598.9 55.60454 8913.008 1796766 51825.38  943718.9 1114.624 8.857672
[4,] 949423.3 56.16282 9068.353 1825084 52292.81  969538.6 1138.865 8.948911
[5,] 971247.7 56.72109 9223.697 1853401 52760.25  995358.3 1163.106 9.040150
[6,] 993072.1 57.27937 9379.042 1881718 53227.69 1021178.0 1187.347 9.131389
         YAM1     YAM2     YAM3     YAM4     YAM5     YAM6     YAM7     YAM8
[1,] 73291.67 681863.6 6979.968 18649.32 25.68650 2.746527 1977.154 74.96959
[2,] 74512.34 697517.8 7103.413 19159.38 24.47304 2.752745 2034.888 73.49074
[3,] 75733.00 713172.0 7226.858 19669.45 23.25957 2.758962 2092.622 72.01190
[4,] 76953.66 728826.2 7350.302 20179.51 22.04611 2.765180 2150.356 70.53305
[5,] 78174.32 744480.4 7473.747 20689.57 20.83265 2.771398 2208.090 69.05420
[6,] 79394.99 760134.7 7597.191 21199.63 19.61919 2.777616 2265.824 67.57536
        YAM10    YAM11    YAM12    YAM13    YAM14    YAM15    YAM16    YAM17
[1,] 54.34051 20671228 13184439 2257.787 816.1503 782.2875 93.11495 206.8584
[2,] 50.88102 20817357 13220250 2243.603 821.2954 787.3863 92.47234 210.5705
[3,] 47.42154 20963486 13256061 2229.419 826.4406 792.4851 91.82974 214.2826
[4,] 43.96205 21109614 13291872 2215.235 831.5857 797.5839 91.18714 217.9946
[5,] 40.50256 21255743 13327683 2201.051 836.7308 802.6827 90.54453 221.7067
[6,] 37.04308 21401872 13363495 2186.867 841.8759 807.7816 89.90193 225.4188
        YAM18    YAM19    YAM20    YAM21    YAM22    YAM23    YAM24    YAM25
[1,] 5673.578 97.12819 9417.815 194.7614 102.9002 12254.22 9204.983 11761.79
[2,] 5765.155 97.06765 9452.625 195.2150 103.0006 12455.54 9359.926 11897.56
[3,] 5856.732 97.00712 9487.436 195.6686 103.1011 12656.86 9514.870 12033.33
[4,] 5948.309 96.94659 9522.246 196.1222 103.2015 12858.17 9669.813 12169.11
[5,] 6039.885 96.88606 9557.057 196.5758 103.3020 13059.49 9824.757 12304.88
[6,] 6131.462 96.82553 9591.867 197.0293 103.4024 13260.81 9979.700 12440.65
        YAM26    YAM27    YAM28    YAM29    YAM30     YAB1     YAB2     YAB3
[1,] 25668.04 571.5277 1241.935 8036.742 75257.06 30346.08 7663.178 604340.6
[2,] 25928.03 584.0608 1264.882 8038.541 75848.96 30883.32 7771.421 620210.5
[3,] 26188.01 596.5939 1287.830 8040.340 76440.86 31420.57 7879.665 636080.4
[4,] 26448.00 609.1270 1310.777 8042.139 77032.76 31957.82 7987.908 651950.3
[5,] 26707.98 621.6601 1333.725 8043.938 77624.66 32495.06 8096.152 667820.2
[6,] 26967.97 634.1933 1356.672 8045.737 78216.56 33032.31 8204.396 683690.1
         YAB4     YAB5     YAB6     YAB7     YAB8     YAB9    YAB10    YAB11
[1,] 78927.45 10382.87 748.2557 705557.0 181028.7 239738.6 40489.41 145355.8
[2,] 79915.56 10580.70 756.3650 719013.6 181947.6 249692.3 41880.88 148553.4
[3,] 80903.68 10778.54 764.4743 732470.3 182866.4 259645.9 43272.35 151751.1
[4,] 81891.79 10976.37 772.5836 745926.9 183785.3 269599.6 44663.83 154948.8
[5,] 82879.90 11174.21 780.6929 759383.6 184704.2 279553.2 46055.30 158146.5
[6,] 83868.01 11372.05 788.8022 772840.2 185623.0 289506.8 47446.77 161344.2
        YAB12     YAI1     YAI2     YAI3     YAI4     YAI5    YAI6     YAI7
[1,] 26369.36 1221.070 39449.62 218.8794 2953.240 758.9790 1884202 22043151
[2,] 26434.73 1251.151 39723.07 220.6451 2977.327 761.9433 1908552 22286045
[3,] 26500.10 1281.233 39996.52 222.4108 3001.415 764.9076 1932901 22528939
[4,] 26565.46 1311.315 40269.98 224.1765 3025.503 767.8719 1957251 22771832
[5,] 26630.83 1341.396 40543.43 225.9423 3049.590 770.8362 1981601 23014726
[6,] 26696.20 1371.478 40816.88 227.7080 3073.678 773.8006 2005950 23257620
         YAI8     YAI9    YAI10    YAI11    YAI12    YAI13    YAI14    YAI15
[1,] 8727.335 279.9258 214690.8 640.2527 1517.996 1059.778 836.3190 253.6565
[2,] 8839.913 289.8530 217242.1 651.6170 1563.793 1081.188 862.5558 260.2159
[3,] 8952.491 299.7803 219793.4 662.9812 1609.590 1102.597 888.7927 266.7753
[4,] 9065.069 309.7076 222344.6 674.3455 1655.387 1124.007 915.0295 273.3347
[5,] 9177.648 319.6349 224895.9 685.7097 1701.184 1145.416 941.2663 279.8941
[6,] 9290.226 329.5621 227447.2 697.0739 1746.980 1166.826 967.5031 286.4535
        YAI16    YAI17    YAI18    YAI19    YAI20    YAI21    YAI22    YAI23
[1,] 142.6639 1302.162 113.8894 38.72376 13.81705 1241.935 3170.028 24.17445
[2,] 146.1278 1332.146 112.9055 39.24739 13.71592 1264.882 3223.635 24.21547
[3,] 149.5916 1362.131 111.9216 39.77101 13.61478 1287.830 3277.241 24.25648
[4,] 153.0554 1392.115 110.9377 40.29464 13.51365 1310.777 3330.847 24.29750
[5,] 156.5193 1422.099 109.9538 40.81826 13.41252 1333.725 3384.454 24.33851
[6,] 159.9831 1452.083 108.9699 41.34189 13.31139 1356.672 3438.060 24.37953
        YAI24    YAI25    YAI26    YAI27    YAI28    YAI29    YAI30    YAI31
[1,] 133170.8 58.14310 525.2985 3942.519 380.6816 147.3531 16.83749 6.507065
[2,] 135147.5 59.52002 533.9327 4045.041 389.6629 150.1061 17.33515 6.634040
[3,] 137124.2 60.89694 542.5669 4147.563 398.6442 152.8592 17.83282 6.761016
[4,] 139100.9 62.27385 551.2011 4250.085 407.6256 155.6122 18.33048 6.887991
[5,] 141077.6 63.65077 559.8353 4352.607 416.6069 158.3653 18.82815 7.014967
[6,] 143054.3 65.02769 568.4696 4455.129 425.5882 161.1183 19.32581 7.141942
        YAI32    YAI33    YAI34    YAI35     YAG1     YAG2     YAG3     YAG4
[1,] 14.30276 8.056203 3.387901 2.856823 241.4434 53.08375 86.71936 11.48687
[2,] 14.40550 8.071011 3.440264 2.861630 245.2879 53.64765 88.77922 11.83379
[3,] 14.50825 8.085819 3.492628 2.866438 249.1325 54.21155 90.83908 12.18071
[4,] 14.61100 8.100626 3.544991 2.871246 252.9771 54.77545 92.89894 12.52764
[5,] 14.71375 8.115434 3.597355 2.876053 256.8217 55.33936 94.95881 12.87456
[6,] 14.81649 8.130242 3.649719 2.880861 260.6663 55.90326 97.01867 13.22148
         YAG5     YAG6     YAG7     YAG8     YAG9     YAG10    YAG11    YAG12
[1,] 116.8489 110.2695 113.6728 188.5472 126.0000  94.10021 363299.0 109407.1
[2,] 118.6982 113.1576 113.8268 189.0959 126.0007  95.80066 370043.2 111576.9
[3,] 120.5475 116.0457 113.9808 189.6446 126.0015  97.50111 376787.5 113746.6
[4,] 122.3967 118.9338 114.1347 190.1933 126.0023  99.20156 383531.8 115916.4
[5,] 124.2460 121.8219 114.2887 190.7421 126.0030 100.90202 390276.1 118086.1
[6,] 126.0953 124.7099 114.4427 191.2908 126.0038 102.60247 397020.3 120255.9
         YAG13    YAG14    YAG15    YAG16    YAG17    YAG18    YAG19    YAG20
[1,]  95625.57 2441.397 30887.95 468320.4 42.03434 613.4947 583.9121 863.2322
[2,]  97300.80 2296.987 31498.02 476763.4 42.64887 628.9947 598.8265 868.3661
[3,]  98976.03 2152.578 32108.08 485206.4 43.26340 644.4947 613.7408 873.5001
[4,] 100651.26 2008.169 32718.14 493649.4 43.87793 659.9947 628.6551 878.6341
[5,] 102326.49 1863.759 33328.21 502092.5 44.49246 675.4947 643.5695 883.7680
[6,] 104001.71 1719.350 33938.27 510535.5 45.10699 690.9947 658.4838 888.9020
        YAG21    YAG22    YAG23    YAG24    YAG25    YAG26    YAG27    YAG28
[1,] 5.692489 10.29121 134.5414 64.33905 22.45877 11.46493 6.117998 7.527294
[2,] 5.784989 10.48246 137.5834 65.57816 22.81770 11.62993 6.236033 7.654616
[3,] 5.877489 10.67371 140.6254 66.81727 23.17663 11.79493 6.354069 7.781937
[4,] 5.969989 10.86496 143.6673 68.05637 23.53556 11.95993 6.472105 7.909258
[5,] 6.062489 11.05621 146.7093 69.29548 23.89449 12.12493 6.590140 8.036580
[6,] 6.154989 11.24746 149.7513 70.53459 24.25342 12.28993 6.708176 8.163901
        YAG29    YAG30     YAC1     YAC2     YAC3     YAC4      YAC5     YAC6
[1,] 7.810328 4.267834 75.49496 28.08939 18.03963 22.73670  97.07023 20.03551
[2,] 7.920685 4.335691 76.48015 28.52898 18.37933 23.38363  98.49098 20.24054
[3,] 8.031042 4.403548 77.46534 28.96857 18.71903 24.03055  99.91172 20.44557
[4,] 8.141400 4.471405 78.45053 29.40815 19.05872 24.67747 101.33246 20.65059
[5,] 8.251757 4.539262 79.43573 29.84774 19.39842 25.32440 102.75320 20.85562
[6,] 8.362114 4.607120 80.42092 30.28733 19.73812 25.97132 104.17394 21.06065
         YAC7     YAC8     YAC9    YAC10    YAC11    YAC12    YAC13    YAC14
[1,] 33.04683 26.11871 39.90827 74401.61 32265.50 53079.34 39696.94 53836.62
[2,] 33.40384 26.60762 40.88681 75021.38 32671.14 54323.88 40309.99 54723.56
[3,] 33.76084 27.09652 41.86536 75641.16 33076.77 55568.42 40923.04 55610.49
[4,] 34.11785 27.58542 42.84390 76260.93 33482.41 56812.96 41536.09 56497.42
[5,] 34.47485 28.07432 43.82244 76880.71 33888.05 58057.50 42149.14 57384.35
[6,] 34.83186 28.56322 44.80099 77500.48 34293.68 59302.04 42762.19 58271.28
        YAC15    YAC16    YAC17    YAC18    YAC19    YAC20    YAC21    YAC22
[1,] 55694.15 26475.44 32479.94 53.45285 31785389 5242.704 2052.823 2000.253
[2,] 57100.60 26814.54 33022.26 54.40587 32129671 5344.422 2088.648 2045.519
[3,] 58507.04 27153.64 33564.57 55.35889 32473952 5446.139 2124.472 2090.786
[4,] 59913.48 27492.75 34106.89 56.31191 32818233 5547.856 2160.296 2136.052
[5,] 61319.92 27831.85 34649.21 57.26494 33162514 5649.573 2196.120 2181.319
[6,] 62726.37 28170.96 35191.52 58.21796 33506796 5751.290 2231.944 2226.585
        YAC23    YAC24    YAC25     YAC26    YAC27    YAC28    YAC29     YAD1
[1,] 1702.062 1830.056 3241.379  909.6797 1593.560 2355.935 2073.892 109.3342
[2,] 1750.128 1856.122 3317.772  928.3638 1638.129 2420.855 2102.779 108.8524
[3,] 1798.194 1882.188 3394.165  947.0479 1682.698 2485.775 2131.666 108.3706
[4,] 1846.260 1908.254 3470.558  965.7319 1727.266 2550.696 2160.554 107.8887
[5,] 1894.326 1934.320 3546.951  984.4160 1771.835 2615.616 2189.441 107.4069
[6,] 1942.392 1960.386 3623.343 1003.1001 1816.404 2680.536 2218.329 106.9251
         YAD2     YAD3     YAD4     YAD5     YAD6     YAD7     YAD8     YAD9
[1,] 36580.69 297.3869 1693.233 490.2888 450.0180 446.6219 896.5404 885.0943
[2,] 36661.39 298.0967 1668.324 490.0699 450.6517 447.2972 897.8461 884.7548
[3,] 36742.10 298.8066 1643.416 489.8511 451.2854 447.9725 899.1518 884.4153
[4,] 36822.80 299.5164 1618.508 489.6323 451.9191 448.6478 900.4574 884.0759
[5,] 36903.50 300.2262 1593.599 489.4135 452.5528 449.3231 901.7631 883.7364
[6,] 36984.20 300.9360 1568.691 489.1946 453.1865 449.9984 903.0688 883.3969
        YAD10    YAD11    YAD12    YAD13    YAD14    YAD15    YAD16    YAD17
[1,] 955.7087 3425.193 37.02926 40.13699 995.3581 23.10254 9.418605 412398.4
[2,] 955.3723 3413.709 36.92033 40.16931 989.3143 23.00504 9.419439 412948.2
[3,] 955.0358 3402.225 36.81140 40.20163 983.2706 22.90754 9.420272 413498.0
[4,] 954.6994 3390.741 36.70247 40.23395 977.2268 22.81004 9.421105 414047.8
[5,] 954.3629 3379.257 36.59354 40.26627 971.1831 22.71254 9.421939 414597.6
[6,] 954.0265 3367.773 36.48461 40.29860 965.1393 22.61504 9.422772 415147.4
        YAD18   YAD19    YAD20    YAD21    YAD22    YAD23    YAD24    YAD25
[1,] 2.328401 1548110 651.7109 26525.37 469.5552 442.8445 328772.6 28062.50
[2,] 2.323576 1544977 664.4261 26609.75 469.1941 442.5369 329724.3 28130.01
[3,] 2.318750 1541844 677.1412 26694.13 468.8329 442.2294 330676.0 28197.53
[4,] 2.313925 1538711 689.8564 26778.51 468.4717 441.9219 331627.7 28265.04
[5,] 2.309100 1535578 702.5715 26862.89 468.1105 441.6143 332579.4 28332.55
[6,] 2.304275 1532445 715.2867 26947.27 467.7493 441.3068 333531.1 28400.06
        YAD26    YAD27    YAD28    YAD29    YAD30
[1,] 315589.0 10219.71 7799.905 56.20913 1038.892
[2,] 316663.8 10185.34 7778.780 56.21254 1050.531
[3,] 317738.6 10150.97 7757.656 56.21596 1062.170
[4,] 318813.5 10116.60 7736.532 56.21937 1073.808
[5,] 319888.3 10082.23 7715.408 56.22278 1085.447
[6,] 320963.2 10047.86 7694.284 56.22620 1097.086

$forecasts$nn
         YAF2     YAF3     YAF4     YAF5     YAF6     YAF7     YAF8      YAF9
[1,] 576129.9 399629.6 369190.5 310621.4 19428079 14894.23 872039.4  690946.8
[2,] 593845.0 407194.7 373771.0 297383.9 19889678 14846.71 874912.2  757369.3
[3,] 607189.2 410556.9 376701.0 291761.0 20187534 14820.07 875197.8  837902.3
[4,] 616972.7 411989.5 378544.7 289168.7 20372329 14805.04 875225.7  924854.1
[5,] 623999.2 412588.7 379692.5 287930.8 20484099 14796.53 875228.4 1000897.2
[6,] 628969.4 412837.2 380402.5 287330.1 20550641 14791.70 875228.7 1051577.6
        YAF10    YAF11    YAF12   YAF13    YAF14    YAF15    YAF16    YAF17
[1,] 885478.4 52.69247 8858.685 1903128 50538.67 860906.2 1051.582 8.705129
[2,] 891006.4 52.14196 9167.226 2095595 50613.07 858070.1 1053.545 8.808936
[3,] 892096.7 51.87789 9381.893 2278130 50660.79 856619.9 1053.922 8.896276
[4,] 892302.9 51.74688 9522.982 2439943 50691.36 855875.4 1053.994 8.968594
[5,] 892341.6 51.68081 9612.072 2573698 50710.93 855492.3 1054.007 9.027651
[6,] 892348.9 51.64723 9666.861 2677231 50723.43 855295.0 1054.010 9.075322
         YAM1     YAM2     YAM3     YAM4     YAM5     YAM6     YAM7     YAM8
[1,] 67970.21 527733.3 6872.615 19039.47 26.84303 2.751403 2026.667 88.99585
[2,] 65400.57 519974.8 6882.853 19108.61 26.83082 2.761346 2104.397 88.99614
[3,] 63624.46 519043.5 6889.310 19112.90 26.82821 2.769901 2154.506 88.99614
[4,] 62382.35 518925.9 6893.367 19113.16 26.82766 2.776973 2184.081 88.99614
[5,] 61506.80 518910.9 6895.911 19113.18 26.82754 2.782609 2200.558 88.99614
[6,] 60886.28 518909.0 6897.504 19113.18 26.82752 2.786959 2209.427 88.99614
        YAM10    YAM11    YAM12    YAM13    YAM14    YAM15    YAM16    YAM17
[1,] 67.13538 19873469 12736949 2789.008 807.8271 787.2340 99.08764 150.8955
[2,] 75.03469 19219714 12636513 2734.170 806.2764 797.1804 98.55969 150.8765
[3,] 79.39368 18610186 12601668 2730.186 805.4983 801.1439 98.44538 150.8765
[4,] 81.20046 18084383 12589153 2729.898 805.1027 802.4366 98.42302 150.8765
[5,] 81.74072 17663585 12584599 2729.878 804.9003 802.8271 98.41874 150.8765
[6,] 81.80326 17348340 12582933 2729.876 804.7964 802.9421 98.41792 150.8765
        YAM18    YAM19    YAM20    YAM21     YAM22    YAM23    YAM24    YAM25
[1,] 5777.407 98.53078 8985.095 199.8189 105.67421 12445.41 9197.845 11467.05
[2,] 5940.211 98.53084 8394.236 175.5178 108.97498 12732.40 9270.378 11424.25
[3,] 6069.735 98.53084 8098.057 154.5581 107.92843 12931.88 9304.305 11411.72
[4,] 6168.739 98.53084 8226.073 178.6678 106.79309 13065.39 9319.808 11407.97
[5,] 6241.977 98.53084 7944.071 137.1498 105.01197 13152.41 9326.816 11406.84
[6,] 6294.793 98.53084 7996.119 141.6610  91.33333 13208.13 9329.968 11406.50
        YAM26    YAM27    YAM28    YAM29    YAM30     YAB1     YAB2     YAB3
[1,] 24888.15 599.4624 1316.287 8167.871 59460.28 31895.90 7567.095 494040.1
[2,] 24788.68 631.4275 1402.223 8343.654 58306.17 34148.56 7515.633 488630.5
[3,] 24766.10 655.0172 1472.375 8576.249 58123.26 36549.45 7494.938 488061.6
[4,] 24760.80 671.4908 1525.551 8879.325 58092.28 39059.67 7489.434 487999.4
[5,] 24759.54 682.5293 1563.409 9256.311 58086.97 41615.87 7488.333 487992.5
[6,] 24759.24 689.7138 1589.085 9680.834 58086.06 44132.84 7488.186 487991.8
         YAB4     YAB5     YAB6     YAB7     YAB8     YAB9    YAB10    YAB11
[1,] 63343.69 10181.67 726.7782 692687.4 150292.9 285008.8 38129.91 141309.4
[2,] 58054.15 10180.40 640.4250 692817.1 150415.7 352639.0 37655.35 141309.4
[3,] 55865.72 10179.91 651.2649 692845.7 150458.1 424797.5 37416.20 141309.4
[4,] 54871.27 10179.73 641.7351 692852.0 150475.9 485454.4 37294.04 141309.4
[5,] 54401.26 10179.66 642.2198 692853.4 150484.0 523558.0 37231.21 141309.4
[6,] 54175.10 10179.63 642.0475 692853.7 150487.8 542221.2 37198.78 141309.4
        YAB12     YAI1     YAI2     YAI3     YAI4     YAI5    YAI6     YAI7
[1,] 26108.59 1365.817 32634.03 294.4203 2545.552 741.1838 1925363 22344329
[2,] 26108.15 1560.061 32634.03 181.1918 2335.916 734.4482 1983224 22772774
[3,] 26108.14 1757.881 32634.03 189.7064 2217.241 731.1924 2033128 23101523
[4,] 26108.14 1935.824 32634.03 408.6785 2144.799 729.5738 2075234 23348615
[5,] 26108.14 2074.118 32634.03 326.2721 2098.642 728.7580 2110078 23531380
[6,] 26108.14 2167.448 32634.03 199.6526 2068.454 728.3441 2138432 23664934
         YAI8     YAI9    YAI10    YAI11    YAI12    YAI13     YAI14    YAI15
[1,] 6937.789 292.2146 214354.7 651.7434 1528.375 1567.905  954.2426 269.1887
[2,] 6937.731 311.9769 215080.2 672.7062 1564.355 2149.030 1046.2306 293.4222
[3,] 6937.731 328.2747 215298.3 695.8552 1586.263 2392.595 1092.0157 319.2736
[4,] 6937.731 340.7545 215362.0 721.6008 1599.176 2432.554 1111.5493 345.7144
[5,] 6937.731 349.7114 215380.5 750.3840 1606.638 2437.250 1119.2823 371.2748
[6,] 6937.731 355.8185 215385.9 782.6440 1610.899 2437.774 1122.2487 394.3606
        YAI16    YAI17    YAI18    YAI19    YAI20    YAI21    YAI22    YAI23
[1,] 141.8072 1236.954 118.3597 38.19209 14.57236 1316.434 3283.556 21.34181
[2,] 142.3412 1220.995 118.3599 38.18806 14.95644 1403.100 3378.347 21.79402
[3,] 142.4433 1213.360 118.3599 38.18600 14.70530 1474.542 3421.019 24.79186
[4,] 142.4625 1209.614 118.3599 38.18495 14.67406 1529.345 3437.935 23.88304
[5,] 142.4661 1207.755 118.3599 38.18442 14.52598 1568.870 3444.275 21.99625
[6,] 142.4668 1206.826 118.3599 38.18414 14.65779 1596.034 3446.600 21.85173
        YAI24    YAI25    YAI26    YAI27    YAI28    YAI29    YAI30    YAI31
[1,] 135350.6 60.35584 461.9917 3917.425 370.2836 140.8873 18.66588 6.580548
[2,] 138067.5 61.85565 461.9294 3948.446 369.5428 139.9294 22.09508 6.630756
[3,] 139718.5 62.36343 461.9290 3960.360 369.1523 139.6550 26.98709 6.638349
[4,] 140674.8 62.52063 461.9290 3964.859 368.9456 139.5741 32.62715 6.639374
[5,] 141212.8 62.56786 461.9290 3966.547 368.8360 139.5501 36.62062 6.639509
[6,] 141510.5 62.58193 461.9290 3967.179 368.7778 139.5430 38.16858 6.639527
        YAI32     YAI33    YAI34    YAI35     YAG1     YAG2     YAG3
[1,] 14.20502 0.5764523 3.415234 2.915355 255.8075 53.36174 90.44052
[2,] 14.20502 8.0911416 3.423249 2.854988 277.6218 54.36572 94.51199
[3,] 14.20502 8.0521662 3.423901 2.880721 301.0986 55.59464 97.02992
[4,] 14.20502 8.0636464 3.423952 2.864459 322.0498 57.13224 98.44976
[5,] 14.20502 8.0606689 3.423956 2.890606 336.7423 59.08049 99.20605
[6,] 14.20502 8.0614707 3.423956 2.856051 344.9509 61.53149 99.59620
            YAG4     YAG5     YAG6     YAG7     YAG8      YAG9    YAG10
[1,]  -0.7424104 117.4431 117.5119 138.3123 205.2227 125.97046 94.03601
[2,]   2.7503375 118.7933 129.9571 249.4868 228.6601 119.46020 95.48166
[3,] -15.3975662 119.4854 145.8678 314.1417 260.3397 107.24141 96.74495
[4,]   4.5816320 119.8257 164.8965 314.1429 300.8127  93.57280 97.83771
[5,]  -3.3058327 119.9895 183.6934 314.1429 345.3421  84.46449 98.77433
[6,]   6.5126533 120.0676 197.1926 314.1429 382.7506  79.60673 99.57063
        YAG11    YAG12    YAG13    YAG14    YAG15    YAG16    YAG17    YAG18
[1,] 369467.3 117733.9 91938.95 6392.685 27724.45 477101.0 36.66600 603.8981
[2,] 379936.6 133597.8 91023.48 6395.348 27555.13 490382.7 36.36359 605.1247
[3,] 387831.1 156740.8 90580.31 6395.480 27533.38 500074.5 36.31865 605.3676
[4,] 393426.3 178306.5 90359.59 6395.487 27530.44 506575.8 36.31152 605.4153
[5,] 397205.7 186424.7 90248.13 6395.487 27530.04 510670.0 36.31037 605.4246
[6,] 399671.6 187848.4 90191.46 6395.487 27529.99 513140.2 36.31019 605.4264
        YAG19    YAG20    YAG21    YAG22    YAG23    YAG24    YAG25    YAG26
[1,] 575.7030 868.8807 5.835026 10.39956 133.9358 64.33589 23.51348 11.50821
[2,] 576.7578 878.2379 6.050107 10.64556 135.4279 64.99738 25.00326 11.62314
[3,] 576.9136 886.2168 6.229625 10.84023 136.3059 65.32885 26.47068 11.68252
[4,] 576.9364 892.9138 6.366072 10.98943 136.8100 65.48921 27.79416 11.71209
[5,] 576.9397 898.4580 6.461526 11.10083 137.0951 65.56544 28.87482 11.72654
[6,] 576.9402 902.9945 6.524099 11.18231 137.2551 65.60137 29.67545 11.73354
        YAG27    YAG28    YAG29    YAG30     YAC1     YAC2     YAC3     YAC4
[1,] 6.480255 7.413213 8.052067 4.468920 77.50816 30.03164 17.54739 24.84884
[2,] 6.956912 7.417947 8.356436 4.713936 80.60747 33.06592 17.51004 27.47467
[3,] 7.380820 7.419627 8.591532 4.911192 83.62120 36.51000 17.50052 29.63155
[4,] 7.713284 7.420222 8.755131 5.051682 86.33030 39.60388 17.49807 31.14708
[5,] 7.944408 7.420432 8.859879 5.141998 88.56045 41.61970 17.49744 32.07841
[6,] 8.090111 7.420507 8.923121 5.195920 90.24459 42.59496 17.49728 32.59876
          YAC5     YAC6     YAC7     YAC8     YAC9    YAC10    YAC11    YAC12
[1,]  99.59882 19.94952 33.08377 26.56850 42.46835 78293.59 32843.91 54383.70
[2,] 103.57301 19.79002 33.45095 26.78380 45.30075 85143.85 33458.96 56632.08
[3,] 107.36655 19.81554 33.78861 26.82432 47.25590 90229.69 33776.93 58503.52
[4,] 110.75977 19.76217 34.09409 26.83162 48.45012 91417.37 33923.01 59976.79
[5,] 113.58705 19.80494 34.36555 26.83292 49.12012 91553.68 33986.20 61081.18
[6,] 115.78524 19.78966 34.60240 26.83315 49.47704 91567.20 34012.79 61876.69
        YAC13    YAC14    YAC15    YAC16    YAC17    YAC18    YAC19    YAC20
[1,] 35292.07 48473.97 57893.49 24468.48 28907.73 54.59223 32157366 5220.007
[2,] 35046.18 47179.70 60694.16 24392.60 28907.71 56.44278 32753465 5282.931
[3,] 35023.97 46782.49 62656.79 24386.09 28907.71 57.97164 33238163 5332.284
[4,] 35021.90 46658.48 63923.25 24385.51 28907.71 59.15435 33624508 5370.510
[5,] 35021.70 46619.57 64693.98 24385.46 28907.71 60.01830 33927422 5399.824
[6,] 35021.69 46607.33 65145.55 24385.45 28907.71 60.62115 34161784 5422.126
        YAC21    YAC22    YAC23    YAC24    YAC25     YAC26    YAC27    YAC28
[1,] 2035.945 2066.710 1649.444 1846.800 3348.197  958.0337 1678.347 2319.630
[2,] 2047.465 2146.437 1647.820 1896.408 3489.286 1042.8240 1788.224 2334.251
[3,] 2054.298 2197.169 1647.235 1955.905 3587.265 1150.9972 1872.445 2341.497
[4,] 2058.289 2226.876 1647.024 2029.889 3649.935 1285.6077 1931.296 2345.034
[5,] 2060.599 2243.373 1646.948 2125.441 3687.766 1439.3877 1969.526 2346.748
[6,] 2061.929 2252.254 1646.920 2253.574 3709.769 1587.3462 1993.109 2347.575
        YAC29     YAD1     YAD2     YAD3     YAD4     YAD5     YAD6     YAD7
[1,] 2047.779 119.3513 36516.57 292.1448 2070.806 503.3429 428.1051 421.9515
[2,] 2048.953 107.4809 36530.35 287.6657 1893.193 475.0069 426.1987 420.9045
[3,] 2048.975 107.3208 36541.78 284.2078 2070.806 467.4423 425.8692 420.7790
[4,] 2048.918 107.3201 36551.25 281.5367 1893.193 471.3604 425.8071 420.7630
[5,] 2048.909 107.3201 36559.09 279.4805 2070.806 477.0578 425.7952 420.7610
[6,] 2048.911 107.3201 36565.57 277.9056 1893.193 486.0251 425.7930 420.7607
         YAD8     YAD9    YAD10    YAD11    YAD12    YAD13    YAD14    YAD15
[1,] 849.7215 883.2025 960.9769 4016.212 36.92678 39.90757 1128.604 23.21975
[2,] 846.8510 866.4815 920.3911 4016.147 36.90650 39.90926 1348.050 23.21981
[3,] 846.4322 847.7006 916.5364 4016.146 36.90490 39.90930 1564.492 23.21981
[4,] 846.3665 870.3796 959.3104 4016.146 36.90478 39.90930 1709.867 23.21981
[5,] 846.3561 872.5563 944.0865 4016.146 36.90477 39.90930 1778.622 23.21981
[6,] 846.3544 880.8414 963.0839 4016.146 36.90477 39.90930 1804.795 23.21981
        YAD16    YAD17    YAD18   YAD19    YAD20    YAD21    YAD22    YAD23
[1,] 9.424835 411165.7 2.303888 1574183 673.5439 26530.15 471.7947 446.1218
[2,] 9.422734 409654.7 2.303888 1572017 683.7699 26579.07 465.2938 446.7210
[3,] 9.423067 408233.5 2.303888 1570400 685.8332 26604.34 439.1285 449.5577
[4,] 9.423018 406761.2 2.303888 1569120 686.2078 26616.98 432.6590 459.7654
[5,] 9.423025 405117.1 2.303888 1568062 686.2744 26623.19 432.6581 468.2079
[6,] 9.423024 403174.2 2.303888 1567160 686.2862 26626.22 432.6581 468.4805
        YAD24    YAD25    YAD26    YAD27    YAD28    YAD29    YAD30
[1,] 325509.2 28108.69 310255.1 5669.615 6662.376 56.08753 1030.708
[2,] 325509.2 28187.76 310254.4 3224.609 5434.229 55.70515 1042.959
[3,] 325509.2 28239.21 310254.4 3224.594 5423.850 55.39880 1052.677
[4,] 325509.2 28271.14 310254.4 3224.594 5423.848 55.19626 1060.050
[5,] 325509.2 28290.35 310254.4 3224.594 5423.848 55.08260 1065.442
[6,] 325509.2 28301.70 310254.4 3224.594 5423.848 55.02543 1069.270
```

---
## seer package: `prepare_trainingset`

```r
prep_tset <- prepare_trainingset(accuracy_set = accuracy_m1, feature_set = features_m1)
prep_tset
```

```
$modelinfo
# A tibble: 181 × 4
 ARIMA_name ETS_name min_label model_names 
 <chr> <chr> <chr> <chr> 
 1 ARIMA(0,1,0) with drift ETS(A,A,N) ets ETS(A,A,N) 
 2 ARIMA(0,1,1) with drift ETS(M,A,N) rwd rwd 
 3 ARIMA(0,1,2) with drift ETS(M,A,N) ets ETS(M,A,N) 
 4 ARIMA(1,1,0) with drift ETS(M,A,N) rwd rwd 
 5 ARIMA(0,1,1) with drift ETS(M,A,N) arima ARIMA(0,1,1) with drift
 6 ARIMA(1,1,0) with drift ETS(M,A,N) ets ETS(M,A,N) 
 7 ARIMA(0,1,0) with drift ETS(M,N,N) rwd rwd 
 8 ARIMA(0,1,0) with drift ETS(A,N,N) nn nn 
 9 ARIMA(0,1,0) with drift ETS(M,N,N) rwd rwd 
10 ARIMA(0,1,0) with drift ETS(M,A,N) theta theta 
# … with 171 more rows

$trainingset
# A tibble: 181 × 26
 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
 1 0.442 0.0400 0.977 0.985 0.985 1.32e-6 4.46 0.705 -0.0603
 2 0.363 0.0790 0.894 0.988 0.989 1.54e-6 4.47 0.613 0.272 
 3 0.379 0.0160 0.858 0.987 0.989 1.13e-6 4.60 0.695 0.172 
 4 0.363 0.00201 1.32 0.982 0.957 8.96e-6 4.48 0.0735 -0.396 
 5 0.156 0.00112 0.446 0.993 0.973 1.80e-6 5.77 1.21 0.0113
 6 0.441 0.00774 0.578 0.986 0.975 3.31e-6 4.75 0.748 -0.385 
 7 0.118 0 0 0.943 0.975 4.95e-6 2.94 0.391 0.0868
 8 0.357 0 0 0.949 0.978 2.39e-6 3.11 -0.360 0.220 
 9 0.698 0 0 0.931 0.983 5.09e-6 2.74 0.381 0.198 
10 0.435 0.0188 1.05 0.987 0.956 8.44e-6 4.70 -1.57 0.445 
# … with 171 more rows, and 17 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>,
# diff2y_acf1 <dbl>, y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>,
# nonlinearity <dbl>, lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>,
# y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>,
# beta <dbl>, classlabels <chr>
```

---

## seer package: `prepare_trainingset`

```r
prep_tset$trainingset
```

```
# A tibble: 181 × 26
 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
 1 0.442 0.0400 0.977 0.985 0.985 1.32e-6 4.46 0.705 -0.0603
 2 0.363 0.0790 0.894 0.988 0.989 1.54e-6 4.47 0.613 0.272 
 3 0.379 0.0160 0.858 0.987 0.989 1.13e-6 4.60 0.695 0.172 
 4 0.363 0.00201 1.32 0.982 0.957 8.96e-6 4.48 0.0735 -0.396 
 5 0.156 0.00112 0.446 0.993 0.973 1.80e-6 5.77 1.21 0.0113
 6 0.441 0.00774 0.578 0.986 0.975 3.31e-6 4.75 0.748 -0.385 
 7 0.118 0 0 0.943 0.975 4.95e-6 2.94 0.391 0.0868
 8 0.357 0 0 0.949 0.978 2.39e-6 3.11 -0.360 0.220 
 9 0.698 0 0 0.931 0.983 5.09e-6 2.74 0.381 0.198 
10 0.435 0.0188 1.05 0.987 0.956 8.44e-6 4.70 -1.57 0.445 
# … with 171 more rows, and 17 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>,
# diff2y_acf1 <dbl>, y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>,
# nonlinearity <dbl>, lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>,
# y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>,
# beta <dbl>, classlabels <chr>
```

---
## seer package

```r
M3yearly_features <- seer::cal_features(yearly_m3, database="M3", h=6, highfreq = FALSE)
head(M3yearly_features)
```

```
# A tibble: 6 × 25
 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 0.568 0 0 0.971 0.995 0.000000237 3.58 0.424 0.412
2 0.745 0 0 0.947 0.869 0.000179 2.05 -2.08 0.324
3 0.423 0 0 0.949 0.865 0.000193 1.75 -2.26 0.457
4 0.513 0 0 0.949 0.853 0.000368 2.87 -1.25 0.281
5 0.553 0 0 0.855 0.586 0.00127 -0.765 -1.77 0.192
6 0.709 0 0 0.964 0.964 0.0000217 3.56 -0.574 0.181
# … with 16 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>, diff2y_acf1 <dbl>,
# y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, nonlinearity <dbl>,
# lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>, y_acf5 <dbl>,
# diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>, beta <dbl>
```

---

## seer package: `build_rf`

```r
rf <- build_rf(training_set = prep_tset$trainingset, testset=M3yearly_features, 
 rf_type="rcp", ntree=100, 
 seed=1, 
 import=FALSE, mtry = 8)
rf$predictions
```

```
                    1                     2                     3 
            ETS-trend                   rwd                   rwd 
                    4                     5                     6 
                  rwd                 theta                   rwd 
                    7                     8                     9 
                  rwd                   rwd                   rwd 
                   10                    11                    12 
                  rwd                   rwd                 ARIMA 
                   13                    14                    15 
                  rwd                   rwd                   rwd 
                   16                    17                    18 
                  rwd                   rwd                   rwd 
                   19                    20                    21 
                  rwd                   rwd                   rwd 
                   22                    23                    24 
                  rwd                   rwd                    nn 
                   25                    26                    27 
                   nn                   rwd                   rwd 
                   28                    29                    30 
                  rwd                   rwd                   rwd 
                   31                    32                    33 
                  rwd                 ARIMA                   rwd 
                   34                    35                    36 
                  rwd                   rwd                 ARIMA 
                   37                    38                    39 
                  rwd             ETS-trend                 ARIMA 
                   40                    41                    42 
                ARIMA                   rwd                 ARIMA 
                   43                    44                    45 
            ETS-trend                   rwd                    nn 
                   46                    47                    48 
                  rwd                   rwd                 ARIMA 
                   49                    50                    51 
                  rwd                   rwd                   rwd 
                   52                    53                    54 
                ARIMA                   rwd ETS-notrendnoseasonal 
                   55                    56                    57 
                  rwd                   rwd                   rwd 
                   58                    59                    60 
                  rwd                   rwd                   rwd 
                   61                    62                    63 
                  rwd                   rwd                   rwd 
                   64                    65                    66 
                  rwd             ETS-trend                   rwd 
                   67                    68                    69 
                  rwd                   rwd                   rwd 
                   70                    71                    72 
                  rwd                   rwd                   rwd 
                   73                    74                    75 
                  rwd                   rwd                 ARIMA 
                   76                    77                    78 
                  rwd                 theta                   rwd 
                   79                    80                    81 
                  rwd                   rwd                   rwd 
                   82                    83                    84 
                  rwd                   rwd                   rwd 
                   85                    86                    87 
                  rwd                   rwd                   rwd 
                   88                    89                    90 
                   nn                   rwd                   rwd 
                   91                    92                    93 
                  rwd                   rwd             ETS-trend 
                   94                    95                    96 
                  rwd                   rwd                   rwd 
                   97                    98                    99 
                  rwd                   rwd                   rwd 
                  100                   101                   102 
                  rwd                   rwd                   rwd 
                  103                   104                   105 
                  rwd                   rwd                   rwd 
                  106                   107                   108 
                  rwd                   rwd                   rwd 
                  109                   110                   111 
                  rwd                   rwd                   rwd 
                  112                   113                   114 
                  rwd                   rwd                   rwd 
                  115                   116                   117 
                ARIMA                   rwd                   rwd 
                  118                   119                   120 
                  rwd                   rwd                 theta 
                  121                   122                   123 
                  rwd                   rwd                   rwd 
                  124                   125                   126 
                  rwd                   rwd                   rwd 
                  127                   128                   129 
                  rwd                   rwd                   rwd 
                  130                   131                   132 
ETS-notrendnoseasonal                 ARIMA                   rwd 
                  133                   134                   135 
                  rwd                 ARIMA                   rwd 
                  136                   137                   138 
                  rwd                   rwd                   rwd 
                  139                   140                   141 
                  rwd                   rwd             ETS-trend 
                  142                   143                   144 
                  rwd                   rwd                   rwd 
                  145                   146                   147 
                  rwd                   rwd                   rwd 
                  148                   149                   150 
                  rwd                   rwd                   rwd 
                  151                   152                   153 
                  rwd                   rwd                   rwd 
                  154                   155                   156 
                  rwd                   rwd                 ARIMA 
                  157                   158                   159 
                ARIMA                 ARIMA                 ARIMA 
                  160                   161                   162 
                  rwd                   rwd                   rwd 
                  163                   164                   165 
                  rwd                 ARIMA                 ARIMA 
                  166                   167                   168 
                  rwd                 ARIMA                 ARIMA 
                  169                   170                   171 
                ARIMA                 ARIMA                 ARIMA 
                  172                   173                   174 
                ARIMA                 ARIMA                 ARIMA 
                  175                   176                   177 
                ARIMA                 ARIMA                   rwd 
                  178                   179                   180 
                  rwd                   rwd                   rwd 
                  181                   182                   183 
                ARIMA                 ARIMA                 ARIMA 
                  184                   185                   186 
                ARIMA                 ARIMA                 ARIMA 
                  187                   188                   189 
                ARIMA                   rwd                   rwd 
                  190                   191                   192 
                ARIMA                 ARIMA                   rwd 
                  193                   194                   195 
                  rwd                   rwd                   rwd 
                  196                   197                   198 
                  rwd                   rwd                   rwd 
                  199                   200                   201 
                  rwd                   rwd                   rwd 
                  202                   203                   204 
                  rwd                   rwd                   rwd 
                  205                   206                   207 
                  rwd                   rwd                   rwd 
                  208                   209                   210 
                  rwd                   rwd                   rwd 
                  211                   212                   213 
                  rwd                   rwd                   rwd 
                  214                   215                   216 
                  rwd                   rwd                   rwd 
                  217                   218                   219 
                   rw                    rw                   rwd 
                  220                   221                   222 
                  rwd                   rwd                   rwd 
                  223                   224                   225 
                  rwd                   rwd                   rwd 
                  226                   227                   228 
                  rwd                   rwd                   rwd 
                  229                   230                   231 
                  rwd                   rwd                   rwd 
                  232                   233                   234 
                  rwd                   rwd                   rwd 
                  235                   236                   237 
                  rwd                   rwd                   rwd 
                  238                   239                   240 
                  rwd                   rwd                   rwd 
                  241                   242                   243 
                  rwd                   rwd                    nn 
                  244                   245                   246 
                  rwd                   rwd                   rwd 
                  247                   248                   249 
                  rwd                   rwd                   rwd 
                  250                   251                   252 
                  rwd                   rwd                   rwd 
                  253                   254                   255 
                  rwd                   rwd                   rwd 
                  256                   257                   258 
                  rwd                   rwd             ETS-trend 
                  259                   260                   261 
                  rwd                   rwd                   rwd 
                  262                   263                   264 
                  rwd                   rwd                   rwd 
                  265                   266                   267 
                  rwd                   rwd             ETS-trend 
                  268                   269                   270 
                  rwd             ETS-trend                   rwd 
                  271                   272                   273 
                  rwd                    nn                   rwd 
                  274                   275                   276 
                  rwd                   rwd             ETS-trend 
                  277                   278                   279 
                  rwd                   rwd                   rwd 
                  280                   281                   282 
                  rwd             ETS-trend                   rwd 
                  283                   284                   285 
                  rwd                   rwd                   rwd 
                  286                   287                   288 
                  rwd                   rwd                   rwd 
                  289                   290                   291 
                  rwd                 ARIMA                   rwd 
                  292                   293                   294 
                  rwd                    rw                   rwd 
                  295                   296                   297 
                  rwd                   rwd                   rwd 
                  298                   299                   300 
                  rwd                   rwd                   rwd 
                  301                   302                   303 
                  rwd                   rwd                   rwd 
                  304                   305                   306 
                  rwd                   rwd                   rwd 
                  307                   308                   309 
                  rwd                   rwd                   rwd 
                  310                   311                   312 
                  rwd                   rwd                   rwd 
                  313                   314                   315 
                  rwd                   rwd                   rwd 
                  316                   317                   318 
                  rwd             ETS-trend                   rwd 
                  319                   320                   321 
                  rwd                   rwd                   rwd 
                  322                   323                   324 
                  rwd                   rwd                   rwd 
                  325                   326                   327 
                  rwd                   rwd                   rwd 
                  328                   329                   330 
                  rwd                   rwd                   rwd 
                  331                   332                   333 
                  rwd                 ARIMA                 ARIMA 
                  334                   335                   336 
                ARIMA                 ARIMA                 ARIMA 
                  337                   338                   339 
                ARIMA                    nn                   rwd 
                  340                   341                   342 
                  rwd                   rwd                   rwd 
                  343                   344                   345 
                  rwd                   rwd                   rwd 
                  346                   347                   348 
                   rw                 ARIMA                 ARIMA 
                  349                   350                   351 
                ARIMA                 ARIMA                   rwd 
                  352                   353                   354 
                  rwd                   rwd                   rwd 
                  355                   356                   357 
                  rwd                   rwd                   rwd 
                  358                   359                   360 
                  rwd                   rwd                   rwd 
                  361                   362                   363 
                  rwd                   rwd                   rwd 
                  364                   365                   366 
                  rwd                   rwd                 ARIMA 
                  367                   368                   369 
                  rwd                   rwd                   rwd 
                  370                   371                   372 
           ARMA/AR/MA            ARMA/AR/MA                   rwd 
                  373                   374                   375 
                  rwd                   rwd                   rwd 
                  376                   377                   378 
                  rwd                   rwd                   rwd 
                  379                   380                   381 
                  rwd                   rwd                   rwd 
                  382                   383                   384 
                  rwd                   rwd                   rwd 
                  385                   386                   387 
                  rwd                   rwd                   rwd 
                  388                   389                   390 
                  rwd                   rwd                 ARIMA 
                  391                   392                   393 
                ARIMA                 ARIMA                   rwd 
                  394                   395                   396 
                  rwd                   rwd                   rwd 
                  397                   398                   399 
                  rwd                   rwd                   rwd 
                  400                   401                   402 
                  rwd                   rwd                   rwd 
                  403                   404                   405 
                  rwd                   rwd                   rwd 
                  406                   407                   408 
                  rwd                   rwd                   rwd 
                  409                   410                   411 
                ARIMA                   rwd                   rwd 
                  412                   413                   414 
                  rwd                   rwd                   rwd 
                  415                   416                   417 
                  rwd                 ARIMA             ETS-trend 
                  418                   419                   420 
                ARIMA                   rwd                   rwd 
                  421                   422                   423 
                  rwd                   rwd                   rwd 
                  424                   425                   426 
                  rwd                   rwd                   rwd 
                  427                   428                   429 
                  rwd                   rwd                   rwd 
                  430                   431                   432 
                  rwd                   rwd                   rwd 
                  433                   434                   435 
                  rwd                   rwd                   rwd 
                  436                   437                   438 
                  rwd                   rwd                   rwd 
                  439                   440                   441 
                  rwd                   rwd             ETS-trend 
                  442                   443                   444 
                  rwd                   rwd                   rwd 
                  445                   446                   447 
                  rwd                   rwd                   rwd 
                  448                   449                   450 
                  rwd                   rwd                   rwd 
                  451                   452                   453 
                  rwd                   rwd                   rwd 
                  454                   455                   456 
                  rwd                   rwd                   rwd 
                  457                   458                   459 
                  rwd                   rwd                   rwd 
                  460                   461                   462 
                ARIMA                   rwd                   rwd 
                  463                   464                   465 
                  rwd                   rwd                   rwd 
                  466                   467                   468 
                  rwd                   rwd                   rwd 
                  469                   470                   471 
                  rwd                   rwd                   rwd 
                  472                   473                   474 
                  rwd             ETS-trend                   rwd 
                  475                   476                   477 
                  rwd                   rwd                   rwd 
                  478                   479                   480 
                  rwd                   rwd                   rwd 
                  481                   482                   483 
                  rwd                   rwd                   rwd 
                  484                   485                   486 
                  rwd                   rwd                   rwd 
                  487                   488                   489 
                  rwd                   rwd                   rwd 
                  490                   491                   492 
                  rwd                   rwd                   rwd 
                  493                   494                   495 
                  rwd                   rwd                   rwd 
                  496                   497                   498 
                  rwd                   rwd                   rwd 
                  499                   500                   501 
                  rwd                   rwd                   rwd 
                  502                   503                   504 
                  rwd                   rwd                   rwd 
                  505                   506                   507 
                  rwd                   rwd                   rwd 
                  508                   509                   510 
                  rwd                   rwd                   rwd 
                  511                   512                   513 
                  rwd                   rwd                   rwd 
                  514                   515                   516 
                  rwd                   rwd                   rwd 
                  517                   518                   519 
                  rwd                   rwd                   rwd 
                  520                   521                   522 
                  rwd                   rwd                   rwd 
                  523                   524                   525 
                  rwd                   rwd                   rwd 
                  526                   527                   528 
                  rwd                   rwd                   rwd 
                  529                   530                   531 
                  rwd                   rwd                   rwd 
                  532                   533                   534 
                  rwd                   rwd                   rwd 
                  535                   536                   537 
                  rwd                   rwd                   rwd 
                  538                   539                   540 
                  rwd                   rwd                   rwd 
                  541                   542                   543 
            ETS-trend                   rwd                   rwd 
                  544                   545                   546 
                  rwd                   rwd                   rwd 
                  547                   548                   549 
                  rwd                   rwd                   rwd 
                  550                   551                   552 
                  rwd                   rwd                   rwd 
                  553                   554                   555 
                  rwd                   rwd                   rwd 
                  556                   557                   558 
                  rwd                   rwd                   rwd 
                  559                   560                   561 
                  rwd             ETS-trend                   rwd 
                  562                   563                   564 
                  rwd                   rwd                   rwd 
                  565                   566                   567 
                  rwd            ARMA/AR/MA                   rwd 
                  568                   569                   570 
                  rwd                   rwd                   rwd 
                  571                   572                   573 
                  rwd                   rwd                 ARIMA 
                  574                   575                   576 
                  rwd                   rwd                   rwd 
                  577                   578                   579 
                  rwd                   rwd                   rwd 
                  580                   581                   582 
                  rwd                   rwd                   rwd 
                  583                   584                   585 
                  rwd                   rwd                 ARIMA 
                  586                   587                   588 
                  rwd                   rwd                   rwd 
                  589                   590                   591 
                   wn                   rwd                   rwd 
                  592                   593                   594 
                  rwd                   rwd                   rwd 
                  595                   596                   597 
                ARIMA                   rwd                   rwd 
                  598                   599                   600 
                  rwd                   rwd                   rwd 
                  601                   602                   603 
                  rwd                   rwd                   rwd 
                  604                   605                   606 
                  rwd                   rwd                   rwd 
                  607                   608                   609 
                  rwd                   rwd                   rwd 
                  610                   611                   612 
                  rwd                   rwd                   rwd 
                  613                   614                   615 
                  rwd                   rwd                   rwd 
                  616                   617                   618 
                ARIMA                 ARIMA                   rwd 
                  619                   620                   621 
                  rwd                 ARIMA                   rwd 
                  622                   623                   624 
                  rwd                   rwd                   rwd 
                  625                   626                   627 
                  rwd                   rwd                 ARIMA 
                  628                   629                   630 
                  rwd                   rwd                   rwd 
                  631                   632                   633 
                  rwd                   rwd                   rwd 
                  634                   635                   636 
                  rwd                    nn                    wn 
                  637                   638                   639 
                   wn                   rwd                   rwd 
                  640                   641                   642 
                   nn                    nn                   rwd 
                  643                   644                   645 
                   wn                    wn                    nn 
10 Levels: ARIMA ARMA/AR/MA ETS-dampedtrend ETS-notrendnoseasonal ... wn
```

---

## seer package: `rf_forecast`

```r
predictedlabels_m3 <- rf$predictions
forecasts <- rf_forecast(predictions=predictedlabels_m3[1:2], tslist=yearly_m3[1:2], database="M3", function_name="cal_MASE", h=6, accuracy=TRUE)
forecasts$mean
```

```
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
[1,] 5486.429 6035.865 6585.301 7134.737 7684.173 8233.609
[2,] 4402.227 4574.454 4746.681 4918.908 5091.135 5263.362
```

---

## seer package: `rf_forecast`

```r
forecasts$lower
```

```
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
[1,] 4984.162 4893.098 4629.135 4199.745 3606.858 2848.873
[2,] 2941.377 2430.512 2028.738 1677.572 1355.680 1052.743
```

```r
forecasts$upper
```

```
         [,1]     [,2]     [,3]      [,4]      [,5]     [,6]
[1,] 5988.696 7178.632 8541.467 10069.729 11761.488 13618.34
[2,] 5863.077 6718.396 7464.623  8160.243  8826.589  9473.98
```